On occasion Quincy will do the same but without the snapping. He just growls and does this drawn out gargle sound. It is more of a startling reaction from being woke up so suddenly. Evidently he doesn't' like having his beauty sleep disturbed.
Maybe you could try to get him to sleep in his bed more often and then once he gets use to that than you can put the bed near your feet where he likes to lay. That way he is in a safe place and you are more likely to be more aware of his presence.