My experience is that the CMs are all aware of what you get when you are on the DDP and are very helpful with your questions.
You walk in, get seated, get a menu, the server usually asks if you are on the DDP, you give them your card (which is also your room key). You order your food. At the end of the meal you will get a "bill" showing what you would have owed if you paid OOP. If you ordered anything that is not on the plan, like alcohol, that will be separated showing what you actually owe.
You can tip in cash or put it on your card. Expected tip is based on what your meal would have cost paying OOP.
The bill also tells you how many TS meals, CS meals and snacks you have left. So it is easy to keep track
After your first day, you will be a pro.