What is a strange behavior is that variables got stuck with a value, even if it is assigned after it's first use... That does not seem to be a compile time assignment.
What does this mean? The behaviour your code displays is what I'd expect; is there some gotcha that you didn't expect?
I think that one has to be careful speaking of compile time in this example; there's the compilation of the program, which happens at (well) compile time, and then the compilation (if that's the right word) of the sub declaration, which happens at run time **. When the sub is compiled, $a has a value, and it's this value * that is compiled into the sub.
* I'm intentionally being a bit sloppy here: as ikegami mentions, closures close over variables, not values; but, as the warning that you quote mentions, the actual variable that is closed over will no longer be accessible at the end of the subroutine invocation, so that there is no further way to change its value.
** Wrong; see below.