To user explicitly has to be assigned department. It's not enough just check all departments. Near each department have to be checked department.
You have in department "Auto assignment" secion enable automatic chats transfer.
By default users sees all pending department chats. To disable that and show only to him assigned pending chats you have to
Developing application takes a lot of time. You can support application by donating. There is no company behind this application and it takes away my free time. Every donation matters and does not matter how small it is!