There are several theories as to how the Austronesian language family ended up so widely scattered. One is a fairly simple migration model: that Austronesian-speaking people and their direct descendents (by and large) moved south from Taiwan through the Philippines and Indonesia before crossing the Indian and Pacific Oceans to Madagascar and Hawaii. That's a bit of a strawman, but it's close enough to the basic idea of the dominant Austronesian migration model. There's been considerable work on this model, and it's really nuanced and evidence-based - it's not speculative or unreasonable. Nevertheless, there are other positions out there. Migration is complicated, and anthropologists supporting the migration view don't rule out other mechanisms. The difference between models is more in emphasis.
Another prominent model of Austronesian spread is the Nusantao model, developed by Wilhelm Solheim, an archaeologist of the Philippines. Nusa is a common word in many Austronesian languages for an island or group of islands (one of the names for Indonesia is Nusantara, which combines nusa with antara, the Sanskrit word for "between", cf. Latin inter, and thus means "between the islands") and tao is a common Western Malayo-Polynesian and Formosan reflex meaning "human" (Filipino tao, for instance) - hence, Nusantao, the "island people" theory.
This model suggests that traits associated with the Austronesian languages and identifiable in the archaeological record were actually the result of extensive prehistoric commerce linking islands throughout northern maritime southeast Asia. There wasn't necessarily any significant migration by Austronesian speakers, this theory suggests. Instead, Austronesian languages in southeast Asia spread through their uptake by non-Austronesian populations, adopting them in order to communicate with Austronesian speakers for trading purposes and to work their way up the social ladder. This is not unreasonable, and a mechanism similar to this seems to have a role to play in explaining the spread of many language families, including Indo-European.
Simplifying the Indo-European picture considerably, it looks a little like this: As the Indo-European-speaking pastoralists of the steppes adopted successful technologies like horse-rearing and wooden wagons, they began to militarily and economically dominate the settled populations to their south and west. They used their horses to conduct quick raids on the crops and towns of the settled Old Europeans, whose populations couldn't successfully defend their lands without the horses to catch the Indo-European-speaking marauders. To be clear, the Indo-Europeans weren't using cavalry; they probably used their horses to ride up, attack on foot, and then swiftly depart. Steppe cavalry armies were an Iron Age invention.
Where could the settled peoples get horses from? Why, trade contacts with Indo-European-speaking people in the steppes, of course! (Steppe horses were bigger than native European horses, according to the archaeological evidence.) This theft-and-trade combo increased the economic power of the Indo-European people (whose presence in the archaeological record is indicated by the Yamnaya horizon), and demonstrated their military power over the settled people. The latter adopted the language and much of the culture of the Indo-Europeans, including religious belief and the complex system of oaths they used*, as well as material culture - largely as a result of Yamnaya/Indo-European-speaking dominance and small-scale migration, rather than after having been replaced by large-scale Indo-European migrations.
J. P. Mallory, a key figure in Indo-European studies, called this the Kulturkugel, or "culture bullet", where the cultural bullet of Indo-European language and culture was shot into Europe, largely discarding the genetic population who had fired it and picking up entirely new populations as it shot into them. Bad metaphor, perhaps. What matters is that the language and culture spread, not necessarily a population. This seems to be applicable to parts of Austronesian spread in southeast Asia as well as the Indo-European expansion.
But it doesn't explain everything, not by a long shot. Indo-European migration along the Danube seems to have taken place due to a literal migration of people - kurgan-building, wagon-riding pastoralists speaking Indo-European dialects literally moving into Bulgaria and Hungary, carrying everything with them. They migrated, and used their advanced wheeled technology to do it.
And of course, the most famous of all Austronesian-speaking migrations, from the islands near New Guinea into the wider Pacific, was not based on the adoption of Austronesian traits by pre-existing populations, because there were no pre-existing populations on most of these islands. Austronesian-speaking pre-Polynesians and pre-Micronesians, assocated archaeologically with the Lapita culture, spread out from eastern New Guinea using their advanced vehicular technology: double-hulled and outrigger canoes. Hawai'i wasn't populated by recruiting an indigenous population into a Polynesian cultural fold; it was populated by Polynesians in outrigger and double-hulled canoes, a group of people who were the progenitors of all humans in the Hawaiian archipelago until the 18th century.
And there are plenty of examples of immigrant communities migrating wholesale in historic times, bringing their language with them and retaining it through the generations (to some extent), and sometimes even maintaining considerable genetic continuity as well. So it's not like migration isn't often a key factor in spreading languages and cultural traits.
Migration is almost never a one-way process, either. It relies on the migrants being aware of a place to migrate to (and so requires some level of scouting or trade before the migration), and it requires both 'push' and 'pull' factors; there has to be a reason for the migrants to leave their homes, and there has to be something about the place they're moving to that makes it more attractive than other places, or at least more attractive than staying at home.** This doesn't necessarily mean that contacts with people back home are severed, and there's no reason to believe that Austronesian (or Paiwanic***, or (pre-)proto-Malayo-Polynesian) speakers leaving prehistoric Taiwan were aware that their descendents would eventually cross the Pacific. They were probably just looking for a suitable place to live. The same is true of Indo-European speakers, many of whom seem to have migrated in the opposite direction after their ancestors had invaded the Danube valley, heading 'back' towards the Black Sea.
It's also true, to some extent, of east Polynesia: Hawaiians made trips to Tahiti for a few centuries after their ancestors had left it, and Tahitians made a few trips the other way (although all such trips abruptly stopped long before the arrival of Europeans).
So when a group of Austronesian speakers went down to settle in the Philippines, there was no reason to believe that some of them wouldn't come back up to Taiwan, especially if the same pressures were on them to migrate (ie, if the pressure was social rather than environmental: endemic warfare, headhunting in particular; competition over wives and bridewealth; disparities in inheritance between younger and elder brothers forcing younger brothers to look for a way to achieve their ambitions elsewhere, etc). Some groups would be forced to migrate, and there's no reason whatsoever to believe that they would only move towards the south.
In fact, this is exactly what we find. Here's an example. The indigenous languages of Taiwan are Formosan, which is defined as being Austronesian, but not Malayo-Polynesian (MP). Malayo-Polynesian is a subfamily of Austronesian that encompasses all of the languages that we find outside of Taiwan, from Madagascar and the Philippines to Easter Island. Formosan is a set of other subfamilies, defined in opposition to MP, and found only on Taiwan. All indigenous languages in and around Taiwan are Formosan - except one: Tao, or Yami, which is a Malayo-Polynesian language of the Philippine subfamily of MP. Tao's parent language was a northern Philippine language, not a Formosan language. Tao doesn't come from Taiwan, except indirectly via MP. That means that the speakers of Tao migrated north after their ancestors had migrated south. The Tao migration was a more recent migration that took place after the proto-MP spoken by migrants from Taiwan had differentiated into subfamilies, like the Philippine family.
The lesson: migration doesn't mean unidirectional cultural or linguistic spread, as the Nusantao hypothesis would claim. I'd say that a general trend of southward migration by Austronesian-speaking people, combined with a series of back migrations and a fair amount of trade, recruitment, and genetic input from non-Austronesian speakers, is consistent with the archaeological data that the Nusantao hypothesis rests on.
The really important thing to remember is that Austronesian and Indo-European spread is fundamentally a linguistic problem. Austronesian-speaking peoples are united almost entirely by speaking Austronesian languages, and not necessarily by genetic continuity with a founding population of migrants from Taiwan. Speaking a similar language implies a strong historical connection, but it doesn't say much, necessarily, about the nature of the connection. On the other hand, there's plenty of evidence of the propagation of all sorts of traits from Taiwan in the Neolithic, including genes, bacteria, and cultural traits (like headhunting and belief in ancestral spirits), so while the Austronesian expansion is primarily about language, it appears that a number of other independent traits tagged along with the Austronesian-speaking population.
The Nusantao position - that Austronesian languages spread by being adopted by previously non-Austronesian speakers in a recruitment relationship with Austronesian-speaking warriors and migrants - seems like a good bet, but only with significant caveats. It's often counter-posed to other theories of Austronesian spread, on the assumption that other scholars espousing an Austronesian migration are essentialising Austronesian language, genes, and cultural traits. I don't think this is necessarily the case.
Austronesian speakers brought a lot of cultural baggage with them from Taiwan. Headhunting was one cultural practice they took with them (found in pre-Chinese Taiwan and throughout island southeast Asia, Melanesia, and parts of the Pacific), along with the sleek, fast-moving outrigger canoes that allowed them to trade with and attack people on other islands with relative ease. They had a military advantage, a cultural tradition (like the Indo-Europeans) of sending young men off to earn their laurels through combat with outsiders, and a series of reasons for wanting to migrate frequently - not least of which was the presence of other Austronesian-speaking headhunting tribes. These people had the means, the might, and the motives to migrate.
But these traits also made Austronesian language and culture a powerful recruiting tool in southeast Asia. Join with the tribe, and we won't cut off your heads - use canoes, talk like us, cut off the heads of our enemies, raise and eat pigs for feasts, grow rice, don't be outsiders. It's easy to see why non-Austronesian speakers would have been struck down by the Austronesian culture bullet.**** It's also a reasonable way to make sense of the fact that many of the areas in which Austronesian populations appear to have been a (genetic) minority on islands with a strong pre-existing local population (especially in eastern Indonesia) also exhibit fairly rigid matrilateral marriage alliances. Marriage alliances recruit other groups by imposing a set of ritual, secular, martial, and economic obligations on them in the form of oaths, pacts, and bridewealth. These alliances were backed up by the threat of headhunting and arson until recently in many areas. Perhaps Austronesian language and lifestyle was adopted by less powerful but more numerous native people in places like Timor through marriage alliance.
Combined with fairly extensive migration out of Taiwan and from founding populations in southeast Asia, this view makes sense of the archaeological, linguistic, and genetic data, which in many parts of the Austronesian-speaking world shows considerable mixing between native and Austronesian-derived populations. This is especially so in the islands of Indonesia east of Bali. It also includes the people who went on to establish Austronesian languages in the Pacific: they picked up their anti-malarial genes from natives of New Guinea.
In any case, migration isn't a simple thing, and the Austronesian language family's presence throughout the Indo-Pacific has no single, simple cause. Archaeological evidence should be interpreted in the light of ethnographic data, and a strong version of the Nusantao model doesn't seem to stand up. Nor does a naive migration model. Reality is, of course, complicated.
* Such as that between Glaukos and Diomedes in the Iliad; they refuse to fight each other after realising that their grandfathers had had a guest/host relationship based on an oath. They end up exchanging gifts instead of killing each other.
** Some migration today doesn't depend on scouts or pull factors; a lot of refugees leave their homes solely because of danger at home and the general belief that other places are better. Many asylum seekers in the UK, for instance, simply boarded a lorry after paying an extortionate amount to a people-smuggler, and didn't care so much where they ended up. Needless to say, this form of emigration has no role in explaining prehistoric migration.
*** Paiwan is the Formosan language most closely related to the Malayo-Polynesian languages spoken outside Taiwan, and so it is theorised that Paiwan and Malayo-Polynesian share a parent, some kind of pre-proto-Malayo-Polynesian, or Paiwanic.
**** Or by Austronesian memes, or Austronesian representations, or whatever other label you like for this.