I would also say that nations here are calling their own shots, and that they are not really aligning with the US or moving into a US camp, rather they are managing their relations across a spectrum of countries in line with their own perception of their own interests... which after all is what anyone would rationally expect.
I don't know how much "influence" the US could really be said to have in SE Asia, at least if we take the OED definition of "influence": the capacity to have an effect on the character, development, or behaviour of someone or something. I don't think we're having any such effect or that we have any such capacity: we're not changing the way anyone thinks or acts, and we're certainly not directing anyone's character, development or behaviour. We (and they) are simply finding areas where interests overlap and working to enhance those interests.
In short, our relations with SE Asian countries are moving into a peer-to-peer mode, more resembling relations with Europe than the old-school patron-client relationships that used to characterize relations with the developing world. That's probably least true in the Philippines, but even there we aren't calling any shots, far less so in the rest of the region.
I'm not at all sure that US influence (defined as above) is rising in the area: we do not have and are not gaining the capacity to persuade or compel any of these nations to do anything they don't want to do or weren't already doing. I also don't think it's accurate to think that the SE Asian nations are joining a US camp or falling in line with a US strategy. None of this is directed or orchestrated by the US; the nations involved are calling their own shots for their own reasons.
China's a long way from making an aggressive play to control anyone in the area, and I'm not sure that's really the concern. Also most of these nations are not really looking to the US as a first choice partner, rather as one partner among several. The Vietnamese, those closest to the perceived problem, engage with the US, but are also engaging actively with India (including proposed joint ventures in offshore energy projects in disputed areas) and other SE Asian nations, while buying most of their arms from Russia. That's true elsewhere in the region as well: most states are not looking for a big brother to protect them, rather to build a network of supporting alliances. Assuming that it's all US-centric is, I think, a mistake.
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