It does not automatically activate the subscription if that's what you are asking.
He would need to activate it himself through the App and will be an additional charge.
This is all assuming he is in fact using his own Apple ID for iTunes & App Stores on his devices and not yours, which would totally defeat Family Sharing, and would be the most likely cause of it saying that Apple ID is already being used.
Verify on his device, that his account is logged in to iTunes & App Stores in Settings, and that he is not trying to log in with your Apple ID in the App.