If it is linked to your reservation it shouldn't ask for payment. If you don't have your US reservation number ring disney UK and they will be able to give it to you.
I think you have to pay in advance for CRT - I know we did (we weren't on the dining plan that time though, back in 2008). I was told when I booked that the payment was just a "hold" and wouldn't be charged unless we didn't show up. However half way through the meal they bought out a credit card receipt out that they had charged to the card details I had given over the phone, which I wasn't very pleased about as its not the card I would have chose to use. So just make sure when you check in that you tell them you are on the DDP so they can sort your refund out/ don't charge you to start with!