Okay, I had a little play around with it, and from my understanding (Which is minimal - i've never used templates) When you use a RunFSM Action, it runs that FSM to completion (for example, until it reaches a "Finish FSM" Action) before moving onto the next task, But, as your first template sends it to another Event, it never gives the inputs to the other templates.
Edit: Additionally, When the host is sent to another event, it disables the template FSM that was running. I don't think it's possible to have multiple copies of the same template accessed by the same host at the same time.
I discovered this trying a workaround, whereby an extra input string was used to send the host to an event starting the next template (So Template 1 would send the host to an event beginning Template 2) before doing it's wait action. Only the final template ran through to completion.