While Nocturne certainly seems like a clear-cut villain, his motivations, from what he's hinted at, aren't entirely unreasonable. Here's the thing: what if he does have a good reason?

After all, he ONLY targeted Summoners and no one else, and a JoJ interview (of debatable canonicity at this point, but I digress) indicates that he truly despises Summoners, and not just because they're enslaving him as punishment for attempting to systematically eliminate them. While this could just be some sort of unfathomable alien hatred for powerful magic users, his threats indicate very human reasons for wanting to kill them. Put some thought into it, and it's quite possible that he has a very legitimate point.

After all, they've demonstrated some truly incredible lapses of judgment by way of enslaving other cosmic horrors and letting known war criminals, terrorists, amoral mercenaries, power-hungry sorcerers, openly malevolent undead, violent psychopaths, and other highly dangerous and/or unstable individuals get a free pass just by agreeing to work for them, and there's no small amount of indication that quite a few of the more powerful individuals in their employ are far too powerful for them to control, so what's to say that he wasn't trying to kill them because of how arrogant, myopic, idiotic, and flat-out morally bankrupt they generally are? The nightmares that plagued them could have very easily been the equivalent of warning shots; when they failed to heed them, he just cut to the chase and killed them. In fact, it's entirely possible that he's an extradimensional policeman of sorts who monitors the waking world through dreams for anything indicating a possible threat to reality, and that the Summoners just so happened to be a big enough threat to warrant lethal force.

police nocturne pls.
But seriously, Nocturne isn't good or evil. He's a primordial natural mechanism to stop bad stuff. Like inter-planar summonings. Like Fiddlesticks and Cho'Gath. Brand is similar to him. They're both primordial forces. The difference is that Brand is drawn here because he's destructive fire. And he knows that a firestorm is coming, somehow.

Because he IS that firestorm. He said HE has purged the world in flames.

And you mean Nocturen is the universe's reaction to summoners to stop more Fiddlestickses from showing up?

Cho'Gath came on his own. Summoning magics might have gotten his attention, but he wasn't summoned to Runeterra, he waltzed in and got captured afterward.

I don't view Nocturne so much as evil, but more as Yang to Yin. A necessary force of balance that in an odd way makes him a good guy.

I think the "INTERPLANETAR POLICEMAN" idea is a bit farfetched, albeit pretty awesome.

He's not good or evil, he just is. He exists, and he gave his existance a purpose: To kill.

Basically an outside force screwed with the summoning and caused Cho to be summoned, not whatever they were trying to summon.
I'd put 5:1 odds on something very similar happening with Fiddlesticks.
Basically Nocturne is like a white blood cell. He sees things and kills them because that's what he's programmed to do, not because he's got any sense of good or evil.
Brand is basically destructive fire. He perverts regular fire into something huge and bad. His physical form isn't nearly as powerful as he really is, I don't think.

Fidds probably was an unintended result of an incredibly dangerous ritual that no one in their right mind should have performed; as for Cho, he wasn't exactly summoned voluntarily, but they still made the decision to enslave him rather than destroy him even though it's heavily implied that he stays bound only because he thinks it's funny that they think they're the ones with the power. So yes, the presence of both of those beings in the League can be attributed to hubris and general idiocy.

Also, Brand definitely isn't evil so much as his goals are completely incompatible with the populated world as a whole. He's a force of nature whose sole mission is renewal through destruction, and as such is completely beyond good and evil. He just is.