Participants are never responsible for payments even if over 18. Her having a titanium card doesn't change that. If you want that to change, she would need to apply for her own Apple Card account.
Also see the following excerpt from Set up Apple Card Family and add a co-owner and participants - Apple Support
What participants can do on a shared Apple Card
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- If they're 18 years or older, they can order their own titanium Apple Card.
- If they're 18 years or older, they can opt in to build their credit and be reported as an authorized user on the account.
If a participant is 18 years or older and doesn't want to be part of Apple Card Family, they can apply for their own Apple Card account.9 If their application is approved and they accept their Apple Card offer, they get their own account and are removed from the shared Apple Card account.