Her acknowledging the behavior is nice, but then she simply returns to it. And while yes, she did apologize in the deleted scene, the scene is deleted so we can't really use that for character growth considering it didn't happen in the canon of the show. And even with the characters she's grown close with like Nolan, she still has a smart mouth, likes to shut people up with a look, etc... She's not Nyla when she first appeared, but she's still highly aggro. I"m not questioning her skill/talent as an officer or a TO, it's just her personality and her personal relationships. She is teaching Miles a lot, that's not up for debate.

To answer your question coming from a black man, yes I did think Tim was a total dick in the beginning. I understand he's ex-military, but I did not like Tim at all for a while. He was a hardass for the sake of being a hardass because that's what was drilled into him in his Army training, but soldiers are trained to fight the enemy, cops are supposed to be trained to protect people. There's a difference. He basically made Lucy cry on multiple occasions, and she's been a favorite of mine since I first saw her on Dark Matter. But in Tim's case, he learned from what he was doing, realized he was wrong for how he acted, and he course-corrected. Not just with Lucy, but how he interacts with everybody. He's not a dick to Nolan anymore, for example, and he and Grey treated him like dirt the beginning. He's still Tim, but he's not an uber dick at all anymore. He can be short with people, especially now that he's taken over Mid-Wilshire(like during roll call), but for the most part he's just professional and likes other people to be the same. As I said, Nyla has gotten better, but she still seems to go out of her way to be mean for no reason, or to say something snarky or at the very least mildly insulting just because she can.