Yes, the P.I. are part of Asia. (I know a lot of folks who refuse to see it that way, and most of those doubters have roots in East Asia.)
It's also important to remember that Austronesians, the predecessors of the Polynesians, set down their roots in places we don't think of as "native." Try Taiwan, where aborigines have lived for thousands of years. One tribe, the Tao, are trying to reconnect with their relatives in the northern part of the Philippines.
Ipanga na and tails and tales of Flying Fish
[Tao] tribesmen constructed a traditional boat (ipanga na; they haven’t built one in over 100 yrs) and made a voyage from Lanyu (Orchid Island) to [Taitung] … in preparation for their voyage back to Batanes [the northernmost and the smallest province of the Philippines] in order to keep [a] tradition from completely dying. … [No] one alive has ever made the trip, but some of the elders still have the oceanic knowledge of the “black current” that runs between Taiwan and [the Philippines] (which is how them used to travel between the 2 islands!) So this journey is very important for them in order to keep the connections alive!
Truly exciting stuff here. It appears, in my limited reading about the native people of Taiwan, that there is fairly good relationship between tribes and the recent invasion of mainland Chinese. How far did the Tao and their cousins in the Austronesean circle travel a thousand, 10,000 years ago? Did they travel further north?
There are some keen similarities in art and ceremonial clothing when you observe the natives of Southeast Asia and the native North Americans. It boggles the imagination.