This is because you are using NAS: "he did not get a message about the client already being open and only having read only access."

NAS is a static storage device and not a self-managed server-type device. The only way to do what you expect is to set up one of the computers as a peer server and attach the NAS to it as a static drive for the Computer to manage. Then, no one else would access the NAS files directly. Which means you would save money and simply use a larger SSD/HD for the server system. Think of a server installation as having a librarian, and no one would want to bypass the librarian.

What you did is set up the NAS as a common library or repository, and this allows you to have common access, but think of this as a swimming pool without a lifeguard. A NAS has no operating system, so it has no way to monitor the condition you describe.

You didn't want NAS; you wanted Server.

What you need to do is introduce Internal Controls. The computer system isn't going to manage this for you. Be your own lifeguard.