I have a low-level DIII prospect considering my DIII Hamline team right now, and I have never put any effort into him at all. He was never even put on the watch list. I didn't know the guy existed until I just looked at my team profile and he shows up on the recruiting tab as considering.

Is this common?

Are there certain criteria that make it more likely to occur?

yes it is common.  This happened to me a few times.  In those cases the recruit probably sent you (and to other desired schools) emails requesting you to review their file.  This player was probably never recruited by any program.  Don't worry though, he will not play for you unless you offer him a ship

Good thing this only happens after signings started, if not this could be a big problem especially at D1 where whenever you look overextended it puts into battles.