Hi all, real noobie question here.
If a villain card says at the end of turn but is played during the end of turn step, do its effects activate?
Thanks
Yes.
More precisely: End of turn effects trigger in the order the objects came into play. Since the card that just came into play came into play after the effect that put it into play, it is still in line to be triggered after all the other end of turn effects trigger.
This also works the same way with start of turn effects.
Usually this works against you, like a Stout Barrel pulling out one of the Hayes brothers who immediately shoots someone, or Omnitron pulling out a drone that starts hitting people, but it can also work in your favor. If Omnitron-X plays a component card at the start of his turn using his Electro-Deployment Unit, you'll be able to use that new component right away, since it'll still be the start-of-turn phase.
So, If the Operative drags out an underboss, that underboss then drags out a thug, who then can have his effect text activate as well?
Seems a little odd. I would have thought that all only cards that were in play at the beginning of the End of turn step would trigger.
Design intent, Mark. Yes indeed, the Operative>Underboss>Thug is what happens, and thats on purpose - part of the Chairman's difficulty.
Your timing is correct there, those chains are intentional. That's why the Chairman is rough.
It's what makes cards like Absolute Zero's Sub-Zero Atmosphere pretty sweet! (Okay, there are no other cards like it, but still… 
)
Except in certain cases, Dawn is a nasty one for it when she chains right, and Original Omni's play at end moving to the start and playing an EPE isn't good either.
Voss, however, is another great target for Sub-Zero Atmosphere…at least until he plays Forced Deployment, in which case if that goes off as normal (as opposed to someone destroying it before his turn), all the Minions will still hit you before you can do anything about it. But any new Minions played on his turn won't be able to do anything till next turn, which is nice :).
Also, if a villain flips during their Start Phase (Plague Rat, for example) and their flipped side gives them a start-of-turn action, this will trigger as it's still their Start Phase. Once you've gone through every one of their current cards in play checking for Start Phase actions and have resolved them all in order, then it's the end of the Start Phase and you move on to their Play Phase. This is good against Dawn's flip mechanic, though, because say H=3, you will need to have two Citizens in play at the start of her turn in order to get her to flip back (once there are five in the trash to casue her to flip in the first place). Dawn is a Citizen herself, so you only need one other to be present at the start of her turn. Her turn begins, oh look there are five Citizsens in the trash, okay she flips - check Start Phase actions on flipped side…okay she flips back if H-1 Citizens are in play. Oh look, we kept Citizen Spring out on purpose so that this could happen - ping, Dawn flips back for the rest of the game and now we can kill everyone :D.
Cool. Makes things super crazy but if that is design intent then bring on the challenge!
Thanks everyone for your assistance!