Both Minions and Toughened enemies follow the same combat rules for taking hit and damage.
What differs them is the amount of Stress (Vigor + Resolve) they have and Harms they can suffer before being out from play.
Minions - Stress is half the associate attribute, if they take single Harm they are out. Toughened - as player characters, Stress values are equal to the associated attribute, but they can survive two Harms before they are taken out of play.
Harming (either Wound or Trauma) is done the normal way, so in your example -
The minion is out if his Vigor becomes 0 no matter if it is from single hit or several light ones. The rule of getting Harm when vigor is 0 applies here.
The toughened can get a Harm if a hit causes 5 vigor damage after armor soak and again if he reaches 0 vigor (via another hit with 5 vigor damage or multiple). I presume you put 11 intentionally, because the enemy can suffer two 5 vigor-damage hits and still be left 1 vigor. Unfortunately, as per the rules it is out, as it suffered 2 harms already. It does not mean it is dead, but incapacitated, disable in some way.