At the very least, there is the integration between the MagicBand and FREEDOM-POS, the point of sale software running at Disney parks.
It could be as simple as the band functioning as a reference to the built-in EFT account called 'play money', which is a stored value account generated on a POS and assigned to a given serial number (say, a disposable wristband, season pass card number, MagicBand number) and either filled with cash to store and deplete, or linked to a credit card to charge indirectly.
It could be as complex as the MagicBand bypassing FREEDOM entirely and interfacing directly with a back-end server that knows the card details, merely racking up charges over time to be periodically charged directly to the customer's card.
Either way, I'd love to get a peek behind the curtain at the Disney IT operations, warts and oddities specifically.