You have a couple of options:
- Turn on Ask to Buy for your son. That way any purchase would first have to be approved by you.
Approve what kids buy with Ask to Buy - Apple Support
- Use Screen Time Restrictions, where you can not allow any in-App Purchases, or even remove the App Store altogether.
Use parental controls to manage your child's iPhone or iPad - Apple Support
The feature you are referring to that allows members to use your purchase method is called Purchase Sharing and that is either on for all members or off. You don't need Purchase Sharing to share subscriptions, it is used to share purchases such as apps, books, or music.
How to share apps and purchases with Family Sharing - Apple Support
Depending on what you are actually sharing, it may be possible to turn off Purchase Sharing where each member uses their own Payment Method. You can fund a childs Apple Account with Gift Cards so they can make their own purchases.
Even setting up Apple Cash for specific members may be a possibility and managed by the Organizer.
Set up and use Apple Cash Family - Apple Support