ApplePay doesn't communicate with Apple through your phone, it presents the card details as a contactless EMV transaction through the card reader, so it's pretty much spot on as an example of how this should work.

Just so you know, EMV can work entirely offline if you need it to, because the reader has the public keys that the card requires to authenticate and vice-versa. ApplePay uses the same NFC standard as regular EMV contactless cards to communicate, it just happens to be a powered microprocessor instead of a radio-powered microprocessor but that's about the only difference. The smart card standard is really old and covers the exact use case of "what happens if I need to use this thing without the Internet because the Internet wasn't ubiquitous when it was developed.