I would allow it. Here's my thinking.
Is the villain "taking an action"?
On My Mark is pretty clearly an "action". That's what the (A) next to it means. So it certainly counts as the villain taking an action even if someone else also takes an action as a result – I don't think that what the other poster said about "who is rolling the dice" comes into play. The villain's taking an action on their turn, and that action is to trigger some other combatant to do something that they wouldn't normally be able to do. If you can envision a villain "doing something" to cause something on the battlefield, it makes sense to think of it as an action (to me).
Does the action "involve an Attack or Hinder"?
This is the gray area, for me. If the villain allows a lieutenant, say, to take a basic action, and they choose to make an Attack or Hinder, does that trigger this criteria? I could see arguments going either way:
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Yes, because it "involves an attack or hinder". I can see this argument if we take an expansive view of the "involves" criteria. The villain's action made possible an attack or a hinder on their turn, and therefore it "involves" an attack or hinder. A weird part of this interpretation, though, is that if, say, the villain allows a lieutenant to do something non-attack and non-hinder, like create a boost or do some plot-level thing, and that, in turn, triggers a hero or the environment attacking or hindering, then the villain also wouldn't get the defense. Nothing in the description says the attack or hinder would have to benefit the villain! What if the action the lieutenant takes in turn allows a third target to take an action? An expansive reading would say that if, at any point in all the triggered events, an attack or hinder happens, the villain wouldn't get the benefit. Not sure I like that, but I could see it being a valid interpretation.
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No, the villain's action doesn't "involve an attack or hinder", even if the lieutenant's does. I could see this argument if we read the power as implying the scope when it says, "If you take an action that...". The character who is "taking an action that involves an attack or hinder" is not the villain - it's the lieutenant. The power specifies "you", not "anyone" or "you or any ally" or something more concrete, and the power does not require or restrict the basic action taken to be an attack or hinder, so I could see the argument that the language implies the "scope" of that assessment is limited to "you" - the villain. Also, I suspect that what the wording is mainly trying to get at is that if you use one of your own abilities that has an attack or a hinder as an effect, you can't stack that with the defensive bonus (there are narrative reasons for this - see below), so I think this is probably the interpretation that is more in line with the ability's concept.
Of the two interpretations, I lean towards the latter. It's simpler, and seems a lot cleaner to adjudicate, since you only have to concern yourself with the immediate action to judge - nothing will happen "further down the chain" that will come back and invalidate the defensive bonus. And it also makes sense from a story perspective:
What does it mean, narratively?
When I think about what these powers mean narratively, the simpler interpretation above feels right. It makes a lot of sense for a villain to hang back, be defensive, and have someone else do the punching. Indeed, that would kind of be the point of the powers, yeah? Narratively, the reason you can't use Fade From Sight when attacking or hindering is because how can you "fade from sight" and still be getting in the heroes' faces, hitting them or dragging them down? But ordering a minion to go attack while the villain fades from sight makes perfect sense, though, and seems very much in line with the sort of build one might envision for a villain's strategies.
The other direction doesn't make as much sense narratively, at least to me. If the villain is "fading from view" while commanding his minions, I envision the villain trying to stay out of the spotlight, secretly issuing orders to his minions so that they do the villain's dirty work, thus granting the villain a defensive bonus. But, what, he can't issue orders to them to attack or hinder? His commands for them to boost each other let him stay largely out of sight, but commands to hinder or attack don't? Doesn't make a lot of narrative sense offhand, but it's hard to be sure until the particular narrative situation gets presented.
Maybe that's overpowered if the original design intent was to absolutely curtail not just the villain but any lieutenants or minions to attack or hinder. But I kind of suspect not. On My Mark risks being underpowered since, presumably, it will most often be used to grant actions to subordinates. It's seldom that a subordinate's actions are more effective than those of the villain themselves, so it feels right to err on the side of cutting the villain a break if they're replacing their own actions with those of their subordinates. And if it's another villain character the action is passed to, well, that makes sense, too – they're stepping aside and letting the other villain jump into the spotlight and get in the heroes' faces, so having a little defensive bonus to represent that shift of focus makes sense. And it gives the heroes the interesting choice between pushing against the "frontmost" bad guy or having to make some sacrifices to go after "the man behind the curtains", so I like the nuance it brings.
So, for me, I'd probably default to interpreting it as a "yes", although I'd probably be open to adjusting it in edge cases if it doesn't narratively make sense in the moment or if it turns out to be too powerful. Basically, I'd ask myself, "Is what's going on making sense with the villain "fading from sight"? If so, yeah, I'd let the defensive bonus be applied and just throttle its usage if it seems to be overpowered with the particular mix of villains and minions.