Expansion card questions: What is the exact timing for the card Espionage? It’s worded as such with the word “when” that has tripped…

Question

What is the exact timing for the card Espionage? It’s worded as such with the word “when” that has tripped up some players. What if, for instance, I draw a Weapons Runner as an encounter card, with two copes of Espionage in play. I decide to trigger both of them, doing enough damage to kill Weapons Runner with Black Widow’s hero ability. Does it die before the surge triggers?

Answer