No, you are thinking of the Somogyi effect! (I think!) the Dawn Phenomenon is exactly what badmedisin says, it's the weird fact that your body pushes out extra glucose to help you meet the day. If you travel to another time zone you will find that the Dawn Phenomenon often continues on your original time zone's body clock, which is disconcerting.
However, it sounds to me simply as though your son just isn't taking enough insulin to cover his night time snack. Insulin does work while you sleep, but don't forget that when you are lying down in bed you are not doing any exercise at all, so you probably need a bit more insulin to cover the same carbs.
Try adding a unit at a time and make sure he has something at the ready in case it goes too far the other way and he gets a night hypo.
Badmedisin - have you tried increasing your night time/long acting insulin? What long acting one are you on? I'm on Lantus and that seems to be quite good for coping with the Dawn wotsit. I had similar probs to you before when I was on Protophane.