I've been getting this popups here and there but it always seems like I'm actually very far from conquest victory. Last occurence for example, my alliance has 36 out of 71 systems. How is this imminent? Or I'm missing something? Thanks.

These messages come at % from victory. IIRC at 50% and 75% (I may be mistaken in exact %).

In your post your alliance is about half requirement, so first pop up makes sense.

I see. Just in my head imminent means something just about to happen, and 50/100 or 75/100 are long way from just about ;)

It might make sense to put it a bit later in specific types of victories, but the reasoning here is to try and give ample reaction time for other players to do something about it, something you can't quite do with a runaway economic, wonder or scientific victory. Capturing twice as many systems as you got leaves some time to react, though, so I'll take it up with the design team and see how this fits into our will to reassess victory conditions.

It's not just the timing of warnings. Why not simply change the message to:

"Player/Alliance currently owns X number of systems/victory techs/wonders/capitals and needs Y more to reach Z victory"

It's much more clear and makes it easier to assess whether focus should be diverted into hindering an opponent empire or not. Like OP mentioned, the wording is really misleading and nearly every player will normally think "imminent" means "I lose if I don't do something about it RIGHT NOW", unless they specifically search for that information by asking other players. It doesn't help that the message is same every time as well.

In fact I'd like if you could see opponent progress whenever you want like in other 4X to make competitive thinking more than pure guesswork, though I wonder if you're saving that for the Espionage expansion? Because EL had a game option that let you change victory tracking to only work when having spies in opponent empire.