Hi,
I think you may be confused with the concept of network ownership and what instance of a given player should maintain, act or react to a given action from the world.
Have you studied the photon demo? even if it's not done in Unity networking, It all is very similar in the concept, so I strongly recommand you give it a go.
Send remote event indeed work as a regular fsm event, only that it's sent across the network to reach other running instances.
bye,
Jean