If you want to get a commendation, do something to make yourself stand out as being commendation-worthy, and avoid doing things that will make you stand out as being not commendation-worthy.

I frequently get commendations as a DPS. And let it be known: I am a decent Black Mage who makes plenty of mistakes. So how on earth am I getting so many commendations!?
  1. My Portrait game is on point. When your fellow players are deciding who to give a commendation to, it shows everyone's Portraits. I aim to make charming, well-composed Portraits, and clearly it's working because I keep getting plenty of commendations despite my middling performance as a Black Mage. If I don't say a word for the entire match aside from "HEWWO" and "gg" and I still get a comm, that strongly suggests that I'm getting it due to my Portrait.

  2. Even before Portraits were in the game, I was getting a solid amount of commendations for my verbal contributions. If you can say something that makes your dungeon run feel less like just another run and more like folks having fun together, you're more likely to get a commendation. Maybe that's something as simple as a joke, maybe it's saying something positive after a wipe, or maybe it's just small talk. Don't limit yourself to just being a model on the screen dealing damage: be a person who others enjoy interacting with! And even if you aren't feeling talky, doing something silly like jumping around or emoting can express your personality, and if others are drawn to that, they'll like being with you more and thus you're more likely to get a comm.

  3. Finally, avoid being negative or overbearing. If I see someone be remotely critical of another player, they're not getting a comm. If I see someone give an unsolicited explanation of mechanics, they're not getting a comm. If I see someone pull when they're not the tank or the party isn't ready, they're not getting a comm. Something rude on your Adventure Plate, no comm. You might see any or all of this as harmless, and if so: that's the point! When it comes to commendations, it doesn't matter what you think, it matters what the person giving the commendation thinks. So if you want them, then get outside of your own head and take some time to consider how others might view your actions; don't accidentally sabotage yourself!
I hope this helps any DPS hoping to get more commendations! ^^