It's all about objectives...
When designing (or interpreting, in the case of published adventures) encounters, you must identify the objectives of all parties involved. Truth be told, one's objective is rarely hold my ground until death.
(There's a nice example of this, though, in DDEX3-10:
"A goblin boss, believing himself to be a 'Knight of Graz'zt' remains diligently on guard.... The goblins consider themselves to be the most important sentinels in Graz'zt's service. The goblin boss and his mounts are spoiling for a fight and do not retreat from intruders.
Much more often an objective might be hold my ground until help arrives, or even do my job, which is standing watch, but really they don't pay me enough to put my neck on the line, so I'm just going to shout and run for help if I'm seriously threatened.
(See DMG p.81 on "Character Objectives" for more discussion of the topic.)
On the NPC side, it sounds like the NPC was put in a position to defend their life or die. Well, removing the threat to the NPC's life should go a long way to de-escalating the NPC. The NPC should be furious, scared witless, or overtly hostile, but likely not combative.
If the PC is unnecessarily (in your view) choosing lethal violence as a means to achieve their objectives, then they do not fear the repercussions of those actions enough (in my view).
This is larger than a one-encounter issue, but you may want to talk to players about the repercussions of entering into combat.
Is it dangerous to their bodily health? I.e. do they actually fear taking harm? If not, consider whether that's an attitude you, as DM, like fostering. See also Dealing with "fearless" players.
Is it dangerous to their immediate objectives? Looping back to what I said about objectives earlier, older versions of D&D routinely had tables for "encounter reactions." If an encounter with an NPC starts on your sheet as "neutral" and shoots over to "overtly hostile" in the span of seconds, think about using a finer scale. 2e used the categories Friendly, Indifferent, Cautious, Threatened, Flight, Threatening, Hostile.
If you chose to adopt that scheme I'd recommend you tell your players you'll be thinking in those categories, you enter each encounter with a starting attitude, you track changes borne of players' actions, and you practice communicating them. I just keep an index card with those words on it and leave my pen pointing at the appropriate one. Moving the pen is a physical reminder to me to change my presentation: furrowing brows, tightening lips, shorter answers, "move along"ing the PCs, &c. The point is, when your PCs start to see identifiable responses to their actions, they'll start to think prospectively about how those actions will be received.
(See DMG p.245 on "Social Interactions," but I think earlier editions actually do this one a little better.)
Is it dangerous to their long-term objectives? 5e has this nice renown system you can use to track how the players will be received. It's a little coarse to use on the individual encounter level, but at the one-per-session level or on the mission-level it can be good to award or penalize one renown point. This can shift encounter reactions or even how you structure your adventures. ("Sorry, we decided to hire the other band of ne'er-do-wells--they leave a tidier wake.")
Alternatively, Adventurer's League modules often have "Story Rewards" built in, which is a nice system to adopt, too. For instance, in DDEX3-5...
A party that chooses to sell the captives to the Duergar slavers gets the Oh What a Slaver You'll Make reward: any Charisma (Persuasion) checks made with commoners in the Hillsfar region are made with disadvantage, any Charisma (Intimidation) checks made with commoners in the Hillsfar region are made with advantage.
If you intend to turn any of these dials, I believe it's incumbent upon you to discuss with players first. I think these are big changes in play- and story-style and should be adopted as a group, not unilaterally.