The main source is 'exists'. It could be tensed or tenseless in various senses. If it is just means 'exists presently/now', then P becomes the trivial thesis that everything that presently exists, presently exists.
It means to exist either in the past, now, or in the future. If presentism is formulated using this sense, the thesis is obviously false, since there are things that have existed at some time or other that do not presently exist, such as Caesar.
The distinction amounts to whether one takes tensed operators like 'Will' and 'Was' as primitive (i.e. not analyzable in tersm of more primitive notions), as the tensed view does, or whether one takes them as analyzable in terms of quantification over times, e.g. slices of a four-dimensional block universe (relative to some way of slicing up the block).
The distinction does not help the presentist since no matter how we view time (tensed or not), and no matter if we accept a distinguished time as "the present", thesis P1 and P2, the two disambiguations of presentism, continue to come out trivial (i.e. trivially true or trivially/obviously false).
I think Meyer's argument relies on the assumption that a possibility operator or anything equivalent can be eliminated in the case of modal ersatzism when analyzing which things (e.g. sets of sentences) are possible worlds. (He mentioned this in correspondence.) But if we assume that it can't, as most including myself believe, then the analogy seems good, in which case the actualist faces an analogous dilemma--trivial truth or obvious falsehood.
Meyer objects that on Bigelow's view, we have not been given an explanation of what the present world's (the sum of all the stuff that exists now) possessing the property of Caesar having crossed the Rubicon has to do with the fact that Caesar crossed the Rubicon. I confess I do not feel the force of the objection since it seems pretty clear to me what the former has to do with the latter. The problem I have with Bigelow's view is that the world can't be the truthmaker for 'Caesar crossed the Rubicon' because it does not necessitate its truth; the world could be such that Caesar did not cross the Rubicon. (Another less serious problem I have is that it seems that the world is the truthmaker for any claim whatever that involves only concreta, so truthmaking is trivialized. Another is that it seems anything whatever has the property of being such that Caesar crossed the Rubicon, but we don't want to say that anything is a truthmaker for the fact. What reason do we have for thinking that it is only the world and perhaps some smaller area of land?)