Looking at the video and based on my limited networking experience, the issue is probably that both camera's are set as the current camera. Since the player you control is spawned/instanced first, and then all of the other network player(s) are spawned, the camera nodes on the other player(s) override the initial Camera2D node.
I would either disable current on all camera's and then in script enable current only on the camera that the player controls, or after all the players are spawned enable current on the camera the player controls. Either way, I think that will fix the issue because it will tell the correct Camera2D node to be the current one.
