If your flight NUMBER hasn't changed, then there is no reason whatsoever to call DME. They track you by your flight number, and they are automatically hooked into the airlines' computers. In other words, if you are flying in on January 1 on ABC Airlines flight #123, they will already know your actual arrival time.
You will be calling them to tell them information they already know.
Of course, if your flight number did change, then you need to call them with your new flight number.
If your flight that leaves Orlando (at the end of your trip) changed at all, you can just tell them that when you arrive at Orlando. When you check-in at the DIsney Welcome Center, one of the things they will autocatically do is confirm your departure information.