The unpalatable answer is don’t keep the zip card in the case of a phone that has NFC payment capability.
Then such a confusion can’t happen.
What would be nice is if TFL could issue a version of the Zip card that could be put into the NFC wallet capability of the phone. To do this they would probably need to issue the card as a “scheme” branded debit card that only works for TfL readers, and handle discounts at the “back end”.
Same as the former Citymapper pass card, which was really a Mastercard debit card that “whitelisted” TfL for authorisation, and hence could be put in an NFC wallet.