The original Dutch system used a very similar approach: the card not only stores the balance, but also a history of taps, and information about the travel products. Your travel history is available on a website, but new trips are only shown after a terminal has asynchronously uploaded your new data.

Fixed terminals (like at a train station) near-instantly upload it, movable terminals (like in a bus) have a bit of a delay and sometimes only upload when the bus arrives back at the depot. It is possible to add new travel products or balance from an app / website, but you have to visit a special "pick-up terminal" to update the card.