Yes, this is not the right way.
-
A staff user is an admin, a mod or both admin and mod.
-
To add a user to the staff group you have to promote the user as an admin or mod (or both).
-
After that the staff group will appears in the Automatic group for that user. You don’t have to do anything else.
If you do not want to grant admin or mod powers to the users you need to create a custom group (with a different name, “staff” is already taken). See here for details about custom groups and category permissions How to use category security settings to control access to content