(On Simple Geographic Association)
If you are versed in Geography, then answering this question should not be a problem at all.
Philippines Is in Asia (An Asian Country)
Geographically, by continental association, Filipinos are Asians because the Philippines is in Asia.
Have in mind that there are only seven continents by most standards: Africa, Antarctica, Asia, Australia/Oceania, Europe, North America, and South America; and which else among these continents does the Philippines may be found but in Asia?
Philippines Is on the Pacific Ocean (A Pacific Archipelago)
Based on geography again, however, this time in relation to the world’s oceans—since that the Philippines is situated on the Pacific Ocean; and because all archipelagos located on the Pacific Ocean may be referred to as Pacific Islands; then Filipinos by association to this geographical detail may be described also as Pacific Islanders.
There are five oceans in the world, based on current, general standards: Atlantic, Pacific, Indian, Arctic, and Antarctic. All the countries in the world are all defined as landmasses—some big landmasses or islands, some comprised by a group of smaller islands collectively called archipelagos. The entirety of the Philippines—an archipelago—is situated on the Pacific Ocean. Therefore, it is technically a part of the Pacific islands. That makes inhabitants of the Philippines or Filipinos in general Pacific Islanders.
The Last Leaf
The Philippines, based on its geographical location, is both in Asia and on the Pacific Ocean, making it both an Asian country and a Pacific archipelago; and this makes the inhabitants of the Philippines or Filipinos in general both Asians and Pacific Islanders—but only in geographical terms. For, if genetic and cultural roots are concerned, the matter is much more complicated and debatable than that.