Assign a player to a specific server

Hi,

In my current setup I have one server and several players.
I would like to change this so that I have 2 servers were players are only visible on one or the other of the servers.

I've done a test with 2 servers and all players are visible on both servers even though the players (Max2Play instances) are all set up to connect to a specific server with the -s option of squeezelite.

I understand that the servers broadcast their presence but apparently even though set-up to connect to a certain server, the players respond to the broadcast.
Both players and servers have fixed IP addresses.
How can I make this work?

Thx.