We've done this and this is exactly how it works.Just show your blue ID a card when you get the bill. You will need to pay list when you book, but your credit card will be credited after they see the card and maybe your photo ID..
We were at CRT Tuesday night, asked for the DVC discount with our blue DVC card and ID, and were denied. It does say 10% off on DVC website. When we contacted a manager, they said Disney restaurants don't have to honor the discounts on the DVC website, and that Disney sometimes doesn't communicate with DVC, and vice versa. A bit shocking that a Guest Services manager said this to me. We attempted to contact manager at CRT but they were not available.