As you didn't mention the version you are using I show the procedure in 3.x.
When the admin creates a new user there is the button to set template permissions.
And here the admin selects which templates the user is allowed to use (you see the checkbox "All themes"?)
And in global permission the admin sets what the user is allowed to do with these templates.
Now, if the user logs in for the first time he has all these templates available.
And in 4.x. it is the same.
So I do not understand your problem.
So obviously the admin did not give the correct rights when creating a new user.
Joffm