I commonly experience this 1. e4 c5 2. c3 d5 3. e5 when I play against theAlapin

In my experience playing in the 1200-1400 range, about half the time when I play 2...d5 against the Alapin white will respond with 3. e5. Just pushing the pawn by instead of capturing.

Previously I attributed this to players in this range knowing just enough about the Alapin to play 2.c3 but not knowing what to do after that. However I did some cursory research on it and found an opening explorer page on 365chess that has some games by high ranking players where they've done it. http://www.365chess.com/opening.php?m=6&n=3541&ms=e4.c5.c3.d5.e5

If you were black in this position, how would you take advantage of 3.e5, which seems from the statistics and lack of mention in the Alapin books/videos to be a dubious move?

Study the Caro-Kann advance.