Hi. What Swiss-G said is correct. The merchant's bank is irrelevant. All that is needed is that YOUR Credit Card's issuing bank has made a deal with Apple and has the ability to detokenize the DAN (Device Account Number) into your PAN (Primary Account Number) which is the one on your real card.
Here, I've made a crude drawing. The red parts must match. You register your card number (PAN) into Apple Pay, and Apple contacts your card's Issuer Processor service to provision a matching token (DAN) into your device to use for payments. (left side of chart)
Thereafter, when you tap to pay, your device sends the DAN token and the OD-CVM (On Device Cardholder Verification Method) flag via NFC comms to the Merchant's Terminal.
If the terminal is updated, it can recognize the OD-CVM flag and bypass the usual contactless PIN / signature limits. Note that this standardized flag can be used by any payment method, not just Apple Pay. If the terminal is not updated, then the limits still apply.
If under (or no) PIN limit, the Merchant Terminal dumbly sends the DAN (it doesn't know it's a token because it looks just like a real account number) upstream via the Merchant's Acquirer service, through the Credit Card Brand (Master /Visa /Amex) to the Issuer Bank's Processor, where it is translated into the real number (PAN) for card Issuer Bank approval. (Alternatively, this translation can be done at the branding level.)
The approval then runs the reverse course back down to the merchant terminal and your device.
At the end of each day, the Merchant Acquirer service totals up sales - refunds, and requests each card Issuer Bank to deposit that much money (minus the Acquirer's and Brand's fees) into the Merchant's Bank, which can be any bank. The Credit Card Brand (Master /Visa /Amex) is responsible for sending a cut of the fees that normally go to the bank, to Apple.