[Justiciar Execution Order: what is the activating event?]

Having checked this out in the Creation Kit I can confirm that these encounters are entirely random with the only condition being that the player is at least level 8. You don't have to have even met a Thalmor, let alone done anything to annoy them.

[Justiciar Execution Order: what is the activating event?]

The only way to get the Thalmor and the Dark brotherhood after you is to complete the main quest up until the point where you slay the first dragon and the greybeards call for you

Based on my own experience I don't see how this can be the case. My character has never pursued the Main Quest short of speaking to a couple of folk in Riverwood and I've just been attacked by a Thalmor group for the first time after nearly 200 hours of gameplay (my Breton is level 47, well into the Thieves Guild quest line and part way into both the College of Winterhold and Dark Brotherhood quests, having spent most of the early part of the game concentrating on exploring and performing tasks for the common folk). I suspect that there might well be multiple triggers for this event, but the only one I can see from recent events is that Ancano, an Altmer at the College of Winterhold, has been taking an interest in my activities as I perform tasks there.