The credits are on your Key to the World (KTTW) card as well as your park tickets and it opens your room door. If you choose it can also be used to charge things to your room.
All credits are acessable from any card that has the dining plan attached to it. I beleive it is fairly standard to have it on everyones card, and if you want it to be only on the adults you would have to ask for that at check in.
When you make your ADR (dining reservations) they will note if you are on DDP or not, but it is almost always the first thing your server will ask.