SQL Server Database Role not working
CURRENT_USER refers to the user role your current login has on the specific database.
For instance i have a user called PlebUser, who has db_owner rights on a specific database A, has no rights (not even viewing) on database B and has generic guest rights (server role public) for my master db (C).
Running Select CURRENT_USER for each of these databases returns me:

A: PlebUser (defined role on my database)
B: Nothing, can't even run it because i'm denied on this DB
C: Guest

You need to check whether you are logged in as your defined user (and not as DBO/SA, whatever admin account you are using to create the new users), and that they are properly mapped to specific databases.
You can do this by checking the server wide security logins, properties on the specific login and check user mapping.