When they first see each other it's very natural for them to flare. What you have to do is float them in the tank, either in the specimen container or a cup they can't get out of, float them for a minimum of one week so that they can get used to the presence of another fish. If needed, float for two weeks. Then when you release her, watch how she interacts with them. If you find she's doing some serious damage like biting off tails and fins completely, yeah take her out and try doing the Time Out session again for two weeks (floating in tank so they can see but not touch). This can also act as a QT period since you need to QT them for the minimum of two weeks if not more.
What I did was acclimate them to my sorority water, change their water from the store cups to my water and then float them. I would usually tether them to the side with a twisty tie or something so they didn't float away and sink under the filter or anything. Then every day or every other I would take my spare cup, fill with water from the tank and put the girl into that new cup. Throw out old water, don't put it back into tank since the whole point of quarantine is to keep the tank disease free!
Then by the time their two week probationary period came to a rest, all the girls were comfortable with each other. Yes, occasionally you will get the random girl that can't be housed in a tank but generally with some patience, they can be housed together.
Tearing, ripping, niping and chasing are all very normal for the fish when they are first introduced to the sorority. There will be body slamming and flaring and more, it's part of their need to figure out hierarchy and you have to let them go at it. Only remove if you find the bully doing some serious damage as I said before, like literally taking chunks out of the fish. But all the nipping and tearing and chasing is all normal and has to be done, usually it lasts about 2 weeks.
There was a small study saying that CT's and red girls were more aggressive however I found that my CT girl was very submissive and my red girl was the sweetest girl in the tank. It's hard to say that one color is more aggressive than the other. It's like saying black people are angrier, that's racist lol. Each fish has their own personality and while some may conform to that, most of them don't.
Also size of the fish doesn't matter either, I had one of my smaller girls be Alpha for quite a while, she was eventually pushed down by a bigger fish but size doesn't control the amount of aggression or submission they have. Same thing in people, just because someone looks big and scary doesn't mean they actually are
Also more about my sorority is in my Betta Log, not this one since this is for my babies rather than my other fish. Although lately it's become about everyone haha. All is well though!