Vampire: the Requiem 2nd Edition actually has a unique way of looking at this compared to VtR1 and the various editions of VtM. Most importantly,
In VtR2, losing Humanity over time represents the Kindreds' alienation from human existence.
Humanity isn't morality
Unlike other Vampire games, Requiem 2nd Edition doesn't have a true morality stat. Humanity in the game represents alienation. Likewise, Chronicles of Darkness 2nd Edition (a.k.a. The God-Machine Chronicle) doesn't have a true morality stat; the game's Integrity stat models psychological strain and trauma.
C.f. BITE ME! How to Write Vampire by VTR2's lead designer Rose Bailey:
Humanity is a vampire’s remaining ties to the mortal emotional experience. It’s the ability to empathize with people, and to act like one of them. […]
The Kindred lose Humanity through self-inflicted emotional trauma. Things that create stress and denial and alienation in normal people drive a vampire closer to relying purely on her basest urges, her Beast. The Beast is dependable. The Beast never makes you feel guilty.
Take a look at the breaking point chart in B&S/VTR2 book — if you're used to the chart from VTM, you'd expect it to list "sins" like lying and stealing; but it doesn't. Instead, you could face a breaking point for joining the Ordo Dracul, or getting hit by a car, or visiting your dad's deathbed to say goodbye. There's a ton of stuff about hurting people on there, too, because a central part of the game is that hurting people is part of your vampiric nature.
The game gives you a good bit of leeway on why exactly violence is so firmly tied to breaking points on a chronicle-by-chronicle and character-by-character basis; generally I emphasize Southern-gothic horror of your darkest passions running wild, or the sense of inhumanity that comes with realizing that, huh, actually that horrible thing you did was easy, casual, comfortable.
There's no special exception for self-defense because the mechanics aren't handling "Was it justified?" — only "What happened and how does it affect you?"
(Where morality and remorse come into it is that they serve as excellent pretexts for spending XP to buy back some Humanity — your Kindred character is actively trying to stay connected to human feelings and values, even though it hurts.)
Breaking points aren't punishments
Breaking points are dangerous. They represent potential loss of yourself — to the Beast, for a vampire; or to the weight of trauma if you're a mortal with Integrity. However, facing breaking points in the game isn't a universally bad thing.
For starters, you gain XP: an immediate Beat for the detachment roll, and most likely a second one later when you resolve whatever Condition you picked up as a result of the roll. (Frenzy is, likewise, worth a Beat now if you fail, or a deferred Beat in the form of the Tempted condition.) These payoffs make up a significant portion of the overall XP cycle creates an incentive to push your character towards a bit of trauma, to ride the edge. Losing Humanity or Integrity is usually worth avoiding, but risking it time and again? That's highly rewarding.
Beyond that, breaking points are an indication that your game session is actually going somewhere. The game wants your character to face this kind of situation in play. Think of breaking points as dramatic beats and roleplaying guideposts — a little attention-grabbing pin to remind you that something important just happened in play.
The example: murder by ambush
In the example, the protagonists ambushed and killed some people they ran into, because they seemed like (supernatural) threats. Assuming your Humanity isn't already at animalistic/monstrous levels, that's going to prompt a detachment roll.
Mechanically, it doesn't really matter whether your character attempts to justify it. VTR2 is never going to ask you to jump to any "objective" moral conclusions about that kind of thing. All the Humanity sub-system says is that this experience was traumatic or revealing in some way.
Whether it's "impassioned" or "premeditated" mostly depends on the situation at the time: was it a thoughtful calculation (however quick it happened to be) or a snap reaction based on some emotional reality of the situation (desperate to escape danger, &c.)? That's all you really need to worry about — and, honestly, if you don't get this distinction down perfect every time, I don't think it'll totally ruin your session. (I also don't think it especially matters if the group forgets to do a detachment roll here or there, as long as the overall flow is working for you.)
How does this mean in-character? Well, if nothing else, the way the kine you stumbled onto died so easily is a pretty strong reminder that you're not quite one of them anymore.
When your character doesn't care anymore
If you're very certain that the experience shouldn't emotionally affect your character at all, you've got two options to represent making their peace with it:
Keep riding the spiral of Humanity downward until it doesn't matter anymore. Basically letting your character's Humanity catch up to their mindset.
For example, a pretty natural consequence of joining the Impaled is that you're going to push down to about Humanity 4-5, where "surviving an experience that would put a human being in the hospital" is no longer a breaking point. Because that's what you do for fun now, all the time. Your character may have higher Humanity now, but it's not likely to last long.
Take a Bane to become immune to that specific breaking point. You gain a new supernatural quirk and the breaking point just doesn't affect you anymore, at any level of Humanity.
This is a good fit for your "sacred assassin" type characters who do nasty things as part of their calling but otherwise strive to maintain their connection to their mortal lives.
(For a discussion of coping strategies employed by mortal characters who routinely undertake violence, see the CofD2 Hurt Locker book.)