Hi,
Indeed you need to ensure that every fsm on your player prefab is checking for "is Mine" flag, including your firing system, without this, you won't be able to make a difference and you'll end up controlling both players.
to turn off fsm, have a "meta" fsm sitting on your player, that knows about the other fsm and can enable/disable them other fsm components based on the "is mine".
also, since when you instantiate a prefab it will always be either mine or not, and never change, you can simply have this logic on each fsm and they disable themselves basically, that works too.
Bye,
Jean