The way I described it was oversimplified. Technically, it's more like your credit card issuer issues a new card with the same number and installs it on the chip in the accessory.

To be able to do it, you have to authenticate with your card issuer in a mobile app, similar to how you might when setting up Android Pay or Apple Pay. The mobile app then uses your phone as a bridge between the issuer and the NFC chip in the accessory so the relevant data can be written in a secure way.

That's not how those NFC cards work. They are payment middlemen. They are full cards on their own and just pass on every charge to your other card. Just like Google Pay.