The times for the dinner package are all typically between 3 and 5 pm - they use demand for the package to fill up times normally empty at the restaurants. It actually works out great for us! We have breakfast in the room or when arriving at the park, graze the carts for lunch, then have a nice sit-down meal at the hottest part of the day. When we're done we still have plenty of time to do rides and shows before going to Fantasmic.
I think the CM was trying to explain to you how the package works. When you have dinner, you'll get a card with the number of people in your party in it. You present this at the backstage entrance near Oscars to get in to the show, but you can only do this if you do the dinner package.