Hello syMemaBare,
While you do have to set up Family Sharing in order to utilize an Apple Music family subscription, you can use the steps below to disable Purchase Sharing so that family members use their own payment method for purchases:
Turn off purchase sharing and stop sharing a payment method
If you're the family organizer and you want family members to pay for purchases themselves, turn off purchase sharing:
1. Go to your Purchase Sharing settings in Settings on your iPhone or iPad or in System Settings on your Mac.
2. Turn off purchase sharing:
• On your iPhone or iPad, tap Stop Purchase Sharing.
• On your Mac, click Turn Off, then click Stop Purchase Sharing.
When purchase sharing is turned off, you stop sharing your purchases and lose access to the purchases made by your other family members. However, you can continue to share subscriptions like Apple TV+ and Apple Arcade, but everyone must use their own payment method for purchases.
You can also find those steps in this resource: How to share apps and purchases with your family
Hopefully that addresses your inquiry.
Take care.