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
I don't think the MAD idea works nearly as well with them as it did with Russia. We always enjoyed a pretty sizeable technological advantage over Russia, we either are loosing that advantage with China or we have already lost it thanks to the 'Felon in Chief.' They know we would never launch unless we were backed to a wall or recieved a first strike. I think they would attack in such a way that we look like we have hope until they gain enough control to prevent us from launching, then they would show who really was in control.
Not necesarily factual, but it's my take on the situation. : )