Thanks for that explanation. Please can you let me know where the setting exists to authorize the specific slave to the slave creator user as you have described?

Or does this automatically happen if the user is just a registered user?

In the back-end, this is the "owner" fiel (latest column in the list of site) or the "site owner" field in the detail description.

This field is automatically assigned to the front-end website and correspond to the "logged user".
So when a user is not logged (anonymous) this information does not exists.
The solution in this case is to create a specific plugin that is called by JMS when creating the slave site and that dynamically create a Joomla user that is assigned to the slave site. So that the slave site become "owned" by a specific joomla user like when the user is logged.