OMMA supports offline synchronization. This means devices do not need internet connection to play synchronously. However, devices must be connected within a local network. If your devices are connected directly to the router (modem), synchronization should work even if you have no internet.
If you have a switch between screens and router, scenario becomes more complex.
We mentioned that devices do not need internet in order to run synchronously. If switch is not connected to router, devices may seem to be connected with each other (via switch), but they can not get IP address from router. In this case, we suggest you to set static IP for devices, so they do not need router to get IP.