Yeah, I'm pretty sure that you have to call.
Oh, make sure the CM understands.... and I mean REALLY understands.... that you want to book the Fantasmic! Dining Package. The CM on the phone tried to tell me that I could book a dinner at Mama Melrose's for 6:00 pm when I knew darned well (thanks to the DIS!!!!) that the dining packages were seatings at 4:00 pm or earlier. I just kept saying "Are you SURE it's the F!DP? I don't think that late of an ADR could be with the F!DP" Eventually he said "Oh, no, wait.. there's a different code" and then he booked us for 3:45. Needless to say, that was the only ADR I made with him and then I immediately called back and asked the next CM to make sure it was the package! Yeesh.