Not directly. They won't be able to see your use your card themselves, but if you turn on Purchase Sharing, anything the try to buy or subscribe to, will automatically be billed to your payment method(s) on file as the Family Organizer (as explained in the support document you posted from), unless they have account balance on their Apple ID available to cover the charge. In which case it will use that before charging you.
If you keep Purchase Sharing turned off, then nothing will be billed to you and you can still share Apple Music with them.