As I understand it, we are talking about the Internet in a smartphone.
This technology turns a smartphone into a kind of banking terminal.
About the smartphone "does not know" how much and so on in your accounts. He can only request information from the bank and send payment orders for the relevant accounts. Well, create the accompanying actions, which is supposed to be done.
Yes, smartphones with contactless payment support do not require an internet connection to make a payment. Roughly speaking, when you add a bank card to your phone, the NFC sensor remembers its unique code.
What happens when you bring your smartphone to the terminal to pay? At this moment, the terminal reads the card code, sends a request to the bank (does the buyer have the amount required to complete the transaction?) And then confirms the debiting of funds. That is, only the store terminal should have been connected to the Internet