Ilan Apple Pay works different technically than most other mobile payment solutions. With for example Google Pay, your card data is in a datacenter and your phone/device gets the tokens through a network connection. While it can cache some tokens, when they are used up, it has to get new ones from the server. With Apple Pay, the card data itself is only inside of the Secure Element of the device. It can generate as many payment tokens as you want, without ever needing a network connection. Only for the initial setup, the device needs to communicate with the Apple Pay servers.
So it works just like your normal card also works (and that doesn't have an internet connection either). Just that the card chip is now emulated by the device.