For 18 or 19 year-olds who play in 11 NHL games: the exemption becomes three years for skaters, or four years for goalies, starting with the season the player plays his 11th game.
When a player 20 or older plays in his first professional game (i.e. NHL, AHL, or any other professional league game), the season in which that game is played counts as his first year of exemption.
(So, playing in an AHL game before you’re 20 — as many juniors players do after their juniors seasons end — doesn’t trigger anything.)
A player 25 or older who plays in one professional game is exempt for the remainder of that season only.