Vader z lead and EP auto dmg?

Bora

I was just wondering, if EP under vader lead (upgraded to Z), damages shocked/rebel/jedi enemies at the end of his turn... Shall he cause tm reduction as well? Cause if that's the case a shocked rebel/jedi could be subject to a double dice roll for a potential 40% TM loss.
Any thoughts?

Bora

Or (much probably) is EP auto dmg not attributed to him, like thermal detonators are not adding to the dmg dealt by a particular character?