Unless they are 17 or younger you cannot set up Ask To Buy.
Request and make purchases with Ask to Buy - https://support.apple.com/HT201089 - Family Organizer receives requests by default, but another parent or guardian can be assigned permission.
In that case you have to ask them to make sure they have adequate Apple ID balance to cover their purchases or tell them you will have to remove them from the Family.
Various ways to pay for items in the iTunes and App Stores.
- Add funds to your Apple ID - "With the payment method that you have on file, you can add funds to the Apple ID that you use for iTunes & App Store and iCloud Storage purchases."
https://support.apple.com/HT208687
- Create and add money to an iTunes Pass - "At Apple Stores and select retailers, you can add store credit directly to the Apple ID that you use for App Store, iTunes Store, and iBooks Store purchases." - https://support.apple.com/HT203021
- Redeem App Store & iTunes Gift Cards, Apple Music Gift Cards, and content codes -https://support.apple.com/HT201209