This must mean that when Harry's Patronus knows that another Patronus is looking for it, it isn't because Harry, say, went back in time and sent himself a Patronus message. (Which would have been problematic on its own: where would the information have come from in the first place? It'd be a stable loop with no reason to exist, and I'd like to think such things don't happen.)

So either someone who has non-time-travel knowledge of Dumbledore's actions sent this message to Harry (and who could have done this?)...

or his Patronus knows this on its own, and it isn't a message after all.

The first option is unlikely, but I am confused by both options. A Patronus isn't actually that intelligent is it? And even if Harry's Patronus is, how would it know that another Patronus is looking for it?