It doesn't have to be an out-right military conquest. They can be subtle and long-range about it, with Chinese investors coming in and opening companies that would hire Filipinos to do various things. With that would come pressure to allow more Chinese "executives" and "technicians" in, along with some bribes to officials to make it easier. At no point would China need to be openly aggressive.
Then if "civil unrest" threatened the safety of Chinese nationals, they could "help".
Yes the US has nukes. So does China. Will the US be willing to trade the major cities on our west coast to stop China taking the Phillipeans? We may find ourselves in that position some day. And the Chinese can wait until we have a prez that would not be interested in the trade