One of the drawbacks of Family Sharing is all charges go to the Family Organizer. Even if a family member has a payment method stored in their Apple Account it won't be used. When I look at my son's purchase history in iTunes I see that his recent music purchases have been billed to me. Apple's Support article is clear about this:
Which payment method is charged for purchases that family members make?
When Purchase Sharing is turned on, everyone's purchases bill to the family organizer's payment method.* If there's an issue with the payment method, the family organizer can update their payment method or add a new one.
If you're the family organizer and you don't want to share a payment method with your family, turn off purchase sharing. When purchase sharing is turned off, you can continue to share subscriptions like Apple TV+ and Apple Arcade. When Purchase Sharing is turned off, everyone must use their own payment method.
But this isn't true. My son's recent charges didn't appear on my credit card even though, as noted above, his purchase history says I paid for them.
It turns out there's an asterisk in the above paragraph. I think that was added recently. The asterisk points to a different support article:
Some purchases aren’t charged to your Apple Account balance
If you're in a Family Sharing group, purchases that you make are charged to your personal Apple Account balance. If you don't have enough Apple Account balance to pay for the purchase, the remainder is charged to the family organizer if purchase sharing is turned on.
Yes, that excerpt is internally contradictory! Ignore the heading, the key information is sort-of here: "If you're in a Family Sharing group, purchases that you make are charged to your personal Apple Account balance."
Basically the Apple Account balance is always used first regardless of Family Sharing status. Whatever exceeds that balance is charged to the primary payment method; for a family the primary payment method is always the credit card of the Family Organizer.
So this suggests that if you want charges to go to a family member rather than a family member, you use their primary payment method to create an Apple Account balance and then enable auto-reload.
Even when the payment is through the personal Apple Account balance the Purchase history will show that the purchase was by the Family Organizer. That is a bug. (Apple's purchase history records are a dumpster fire.)
An Apple Account balance can be created through a gift card. But what about using a family member's debit card to add money to their Apple Account? What about using Apple's Auto-reload feature?
Great questions! There's not any good documentation. I don't yet know the answer to the first question, but I did discover what happens with Auto-reload. Even if the family member's debit card is associated with their account the auto-reload will use the Family Organizer's payment method. (In my testing it took over 2 weeks for the first auto-reload charge to actually show on a credit card statement.)
So, what does this mean for those of us who would really like to have family members pay directly for their purchases? So far, not much. If you use auto-reload it may be easier to track the auto-reload payments and not worry about the per-item charges, but that's a small benefit.
That's all I know so far!