I was initially wondering about this too.
Actually, I was thinking about it the other way around: that maybe Harry had to make sure not only that he arrived earlier than the time he recorded so he'd be there for Minerva to find, but also that he arrived after the time of the communication to avoid there being two Harrys for the Patronus to find.
But putting it that way made me realize that no, clearly that isn't a problem: the Patronus (did/does) find the Harry in Azkaban, regardless of what else might be true.
As you point out, we don't know how it did so... maybe it flipped a glowing animal-headed coin... but we know it did so, by observation, and Harry does too.
- This thread has run its course. You will find newer threads in the discussion section.
Another discussion thread - the fourth - has reached the (arbitrary?) 500 comments threshold, so it's time for a new thread for Eliezer Yudkowsky's widely-praised Harry Potter fanfic.
Most of the paratext and fan-made resources are listed on Mr. LessWrong's author page. There is also AdeleneDawner's collection of most of the previously-published Author's Notes.
Older threads: one, two, three, four. By tag.
Newer threads are in the Discussion section, starting from Part 6.
Spoiler policy as suggested by Unnamed and approved by Eliezer, me, and at least three other upmodders:
It would also be quite sensible and welcome to continue the practice of declaring at the top of your post which chapters you are about to discuss, especially for newly-published ones, so that people who haven't yet seen them can stop reading in time.