Additional credit card in Apple one family plan
How can you have an adult family member add their own credit card /Apple Pay to their purchases in Apple one Family so that I am not paying for all their in app purchases.
Your question is not very clear.
Apple Pay is not used for in-app purchases generally. Users can add cards to the Wallet App for use with Apple Pay in stores, websites and apps that support Apple Pay (through the Apple pay button directly)
For in-app purchases, when in Family Sharing (Apple One is not directly related to this) with Purchase Sharing turned on, Family members purchases will be charged to the Family Organizer directly. Family Sharing members cannot use their own credoit or debit cards added to their Apple ID.
You can turn off Purchase Sharing so each family member pays for there own purchases using credit or debit cards added to their Apple ID (can use payment methods added to the Wallet app also). Or if you want to maintain Purchase sharing turned on, family members would need to have Gift Card credit balance on their Apple ID so purchases are charged to that before using the Family Organizer's payment method.
click here ➜ What is Purchase Sharing - Apple Support
click here ➜ Apple Pay - Apple