Whatever you do...DON'T say ADR to a CM on the phone. They will have NO idea what you're talking about. Just tell them you need to make your dining reservations.
You can make them all at once if you have several and with each reservation they will give you a confirmation number...write it down, along with the date and time, etc. Keep this info with you and you also might want to call once and confirm them before you go. All they need for that is the number they gave you. Take the numbers and all info with you to each meal, b/c once in a while they make a mistake and can't find you in the system. Better safe than sorry. Making dining reservations is easy and once you've done it, you're a pro. I've never had a bad CM, so you should be fine!
ETA:
If you're unsure about anything, go ahead and make the reservation. If you're going during
free dining you WILL need ADR's and its best to make what you can in the very beginning. You can always call back to get a better time later, if its available. Once you're there, it will be darn near impossible to get a table almost anywhere but the most out of the way places.