I can tell you from playing Tropico 4 on PC that the money from exports doesn't come when the message on the screen shows you have exported goods. It comes when the dockworkers take wheelbarrows from the warehouse on the dock to the actual ship. When they do this the stock of crates on the dock will diminish and you will get the money. By the time the ship leaves the dock and the message shows how much you have exported you have already gotten the money.
If you select the dock and watch the dockworker and the exports list you should see it working. That being said, there could be an issue with the Xbox that is screwing you over.