Having some playmaker issues so cannot do in front of me, this is off the top of my head so I hope its right
What I tend to do is;
I have 2 Game Objects;
* Character (With animations component)
* Health manager
On the character FSM I would have set "Get Owner" action and set Global Variable to something like "PlayerGO"
You could then have the listener action "Listen_For_Death" - Create a global event "Player_Death_Animation"
This then leads to the next state "Player Died Animation"
Set the action Play Animation - Select the death animation you want to play. (This must be in the animations list in the component)
On the Health Manager, when you get to the action were you want to play the animation.
You do a "send event" action, set the PlayerGO global variable as the target Game Object. The FSM you want to use on that player Game Object and then the global event