Actually, the problem is that only those user types that have access to management of the media library in WP will see the more than the basic uploader.
This is a WP security feature that is not related to ACF or the other plugin you mention. In order for users to see the same thing that the admin uses you need give them the permissions to do so. I am not familiar with the plugin you mention, but it requires giving them the permission to edit posts and upload files, and possibly other things as well. Basically you need to give them all most of the permissions that an “Editor” has.
