Q: Why am I paying for my family members other itunes downloads

If you have setup Family Sharing, this support document explains, but you have setup for a shared billing account. Family Sharing - Apple Support

Excerpt:

Making purchases is easy. So is setting limits.

All new iTunes, iBooks, and App Store purchases initiated by family members will be billed to the family organizer’s account. But the organizer can still call the shots. Just turn on Ask to Buy for children in the family. When a child initiates a purchase, an alert is sent to the organizer, who can review the item and approve or decline it right from the organizer’s device. This applies to both purchases and free downloads.

It is about how Family Sharing is set up. I've not read that much about it, since I don't use it, but it is more for setting up accounts for minor children. If a member of the family sharing has a payment method on their iTunes account, I've heard that it will take from there, rather than the family account, but I cannot be sure of that. Maybe someone else with experience having adult members of the family sharing can provide an answer.

Okay, I followed the link in Family Sharing about purchases. Then followed to the link about iTunes billing. How iTunes Store purchases are billed - Apple Support  According to that, it seems if the member has iTunes gift card balance, or store credit, it is billed to them instead of the family organizer.

About Family Sharing purchases

When you initiate a new purchase, it bills directly to the family organizer's account, unless you have gift or store credit.

First, your store credit is used to pay the partial or total bill. The remainder bills to the family organizer.

iTunes Store credit on your account isn't shared with other family members. So if the family organizer has a $50 credit on their account and another family member initiates a purchase, it won't deduct from the organizer's iTunes Store credit, but bills the payment method that the organizer has on file.

The family organizer gets the receipts for any of their family member's purchases.

Not necessarily. Have them purchase an iTunes gift card for their account, and it will use that balance before it goes into your credit card. It is simple if you read the last explanation that I provided.