dang, good question...
I can vaguely remember reading something about this too from back in the day.

On the one hand - a player might argue, for the hypothetical piece brought in via reserve, that piece has not yet had a unique ally defeated during it's time on the field. So, it's a counter-trigger ability.
Conversely,
other players might argue that it is a conditional ability, requiring only 'at any time during the game' that a unique ally was defeated, so the reserve pieces brought in later would already "hit the ground running" with their impulsive stuff (this can be rationalised by a narrative: They were called in via the holonet, and told prior to arriving that the enemy had killed their |insert unique character name here|, this does happen in real life, such as in conflict, war, or policing duties etc )

I think the former approach -
it's a counter, which happens while a piece with Impulsive etc, is 'in play', is the official one,
so keep that in mind if you go to tournaments and stuff like that.
but either would work, and certainly the latter has been used as a houserule
(usually, its only an extra attack or a little bit of extra damage, or in the case of "Impulsive Internal Strife" or "Impulsive Savagery", it can be a negative for your opponent... and usually when it's triggered, its because a high-point unique beatstick is dead, and 'game over' is not far away hehehe).

Consistency and fun are the name of the game hehe, so whichever way you opt to go for that,
stick with it if it comes up again in the same match.

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How does your approach change,
if we add to the hypothetical:
prior to the reserves piece entering the game - the squad only had one other unique figure, and there's no way to add another unique piece later?
ie, there was only ever 1 other unique character to trigger a beneficial Impulsive ability?
In that exceptional case, I'd be more inclined to let the player use the beneficial impulsive ability.

It's not spelled out in any of the rulebooks, nor in some of the previous rules discussions I could find using google advanced search here or on the WotC forums (via Wayback Machine).