The tokenization handling happens upstream. FirstData, MasterCard etc. (tier 1 processors) know what to do with it. The whole point is the store shouldn't know or care about the credit card. Just that it was accepted or declined. Obviously if the store doesn't take MC or Amex then it reads as an invalid card as usual.
Apple Pay isn't some mystical new idea. The way they do tokenization is clever but the general methodology has existed for a while. The consumer end is just regular NFC as credit card companies, Google and Softcard have been doing for years.
Didn't say it was mystical or new.