How to correctly share a folder?
You have just identified why directories were invented to allow one server to define for a group of computers what users belong to which groups so that when sharing files, the permissions match so that computer Y will see the restrictions hosted from computer Z properly.

The first step is to decide how and where you will enforce the mapping of users to groups so that you can then set up sharing in a way that will work for you.

You'll want to decide if unix permissions (number based users and groups) is workable or if you need real ACL. Nothing prevents you from setting up each computer to mirror the others, but this doesn't scale well as you add people and computers.