Hello @zelterNN,
After some research, I have details to help explain what is going on and to help you get to the permission controls you want 
So Retool has some 'fun' quirks to permissions, because there are two systems of permissions at play.
One system is the 'group' system, which is interfering with the other system. The other system is the 'direct share' system, which I imagine you are trying to use for individual permission for a single user of a single app.
When you share an app the user becomes a part of the "All Users" group for your organization, automatically.
This is why the new users is in the 'full access list', as that list includes them and all members of the current "All Users" group which have access to all apps.
This can cause some confusion, as by default, the "All Users" group will have permission access to all apps in the org. This is a point of contention as this is unintuitive and there are arguments for and against having the default permissions be wide vs narrow.
It sounds like this you do not want new users added to your org to have unlimited access. You can limit this by editing the "All Users" permission group.
This way, when you share a single app, the user is added by default to "All Users" group, but this group will have its permissions limited and will not give the user access to all other apps. The 'direct share' system will give them only access to the specific app that was shared 
To change the permissions of the "All User" group, go to "Settings"->"Permissions" and click the three dots on the far right side of the group row.
Then, at the top where it has "Select Access Type" you can toggle out of the default and select "Define specific app access", and from there use the check box toggles to set up the permissions you want for all users(ie all users in this group)
I apologize for the confusion, we are continually looking to improve our docs and the sharing instructions to better explain this and help users to navigate the permission controls to set things up properly and understand the default behavior in Retool 