I believe U.S. rule over the Philippines can be more likened to manifest destiny over a desire to have more influence in Asia. The Treaty of Paris handed the Philippines over to the United States at the end of the Spanish-American War and it may have been obtained over influence but it was never fully used for these purposes.
America was a controlling freak that hated immigration, much like today, and wanted to keep the Chinese out. We also realized the benefits of imperialism. It may not have been a bad thing, but it wasn't manifest destiny, although there probably are many who also claim it was bad. I'm reserving judgement.
Manifest destiny was really based on the idea of one nation shore to shore, i.e. from the Atlantic to the Pacific on the North American continent. The Philippines was really never part of this vision. The U.S. never intended to integrate the Philippines into the United States as with the west and was more about counteracting potential European rivals in Asia than anything else.
If you have every been to the Philippines, you can see American culture just about everywhere you look. It is a very unique blend. But this isn't done out of manifest destiny. It was just to have and maintain more control in Asia, like we do all over the world.
No, this was not part of manifest destiny, because that said that we should push west in the frontier days and own all of current US. The control over the Phillippines was just so that we could fix a lot of the problems that they had going on over there.
The United States rule over the Philippines was a way for our country to have more influence in Asia. This was a smart idea on the part of our government as well because diplomacy and trade with Asia has created a lot of profit and reciprocal relationships we otherwise would not have had.