Cody holds up a selection of MagicBands for the Johnsons once they arrive in the Magic Kingdom, and they each take one from him at random. In reality the MagicBands would have already been assigned to each family member and shipped to the house long in advance as they had booked rooms at one of the resort's hotels, and would have been needed simply to get inside the Magic Kingdom in the first place as park admission tickets are linked to them.
The Johnsons move across the Magic Kingdom, Epcot Center, and Animal Kingdom as if they're all one huge facility even though each of those individual parks are at least four miles apart from each other.