How does Apple Pay associate rewards card with payment?

One of Apple Pay's strongest features is its security. From what I understand, the only time a credit card account number ever gets transmitted is at registration time - in order to create a special "account id" that is stored, encrypted, on the CPU's "secure element". Thereafter, when one pays with a card, only that card's id plus transactional data (e.g. amount of charge) is transmitted through the sales terminal to the credit card company.

If that is the case, how will Apple Pay work with rewards programs? I'm not talking about store-branded credit cards - presumably the store's sales terminal can recognize those by distinguishing features in the account id being passed - but about simple rewards cards: e.g. the Starbucks Card. If I use my American Express to pay for my drink at Starbucks using Apple Pay, how does Starbucks recognize that I'm a Starbucks Card holder and give me credit for my purchase?

(I realize that Starbucks doesn't yet actually accept Apple Pay - feel free to substitute "Walgreen Rewards" or other rewards program)

As an aside: I've made "Discover Card" my default Apple Pay card (they have an awesome 10% back until end of year for using Apple Pay). The Starbucks app now lets you reload your card using Apple Pay. But when I did, it charged another card (the one I have registered with iTunes) rather than the Discover. The next time I reloaded, I paid a bit more attention and explicitly selected "Discover" on Starbucks' Apple Pay payment screen. It returned a message tot he effect that the card I tried to use is not authorized for in-app purchases. This makes it sound like Discover decided not to allow it. Or is it something I must enable somewhere?