The Edge does not monitor kids leaving. They can come and go as they please. Your child can go to the Oceaneers spaces until they turn 13 so if your child is 11 or 12 and you have concerns about them coming and going from the club, then you can just have them attend Oceaneers and not give permission for self-check out.
Otherwise, you can set strict ground rules with your child. You can either use the Navigator app on a smartphone or the Wave phones for communication. Tell your child to call or text you anytime they are wanting to leave the Edge. Be aware that not all Edge activities take place in the Edge club. They sometimes go up to the sports deck, down to the D Lounge, to get ice cream from the pool deck, or even out on scavenger hunts around the ship.