Usually only printers with a local port will display to all users. (in example with a tcp/ip port), thus I would check why the behavior is not the same for you on your server, I would think that those users are in the local admin group or in the print operator group.
In a extreme way to resolve your issue;
Prevent by GPO to add any printers and deploy by GPO the needed printer ?
Option 1:
In Group Policy editor, expand the following folders: User
Configuration, Administrative Templates, Control Panel, and Printers. (see there)
Disable the addition of printers:Prevents users from using familiar
methods to add local and network printers. This policy removes the Add
Printer wizard from the Start menu and from the Printers folder in
Control Panel. Also, users cannot add printers by dragging a printer
icon to the Printers folder. If they try to use this method, a message
appears that explains that the action is disabled by a policy.
Option 2:
You can configure point and print restriction too, to restrict which the user can add or not. You need to enable the settings, see there for a explanation. Description of the Point and Print Restrictions policy setting
If the driver is not listed it will prevent the printqueue to install with the above setting;
Policy setting: Prevent Users from Installing Printer Drivers
Location: Computer Configuration\Windows Settings\Security Settings\Local Policies\Security Options