They do, but the timing of this makes it seem like a more typical firing. Carole filmed the reunion and announced she was leaving immediately afterwards. They film those reunions for 12+ hours; no producer is really in the right frame to declare that evening that Carole had to go. It's not totally clear that Carole quit, but it's more likely than not that she did. Heather had been hinting about quitting before before they taped the reunion and ratcheted it up after they filmed the reunion. She announced her departure right after the reunion aired. I think she also quit.
I think Dorinda was given an ultimatum that she had to go to therapy and/or rehab and it had to be part of her storyline next season. I think Dorinda quit rather than officially admit that she has an alcohol problem, problems with other substances, and other behavioral health issues. Dorinda kept harping on the difference between Lu's drinking and her own. Getting arrested is this clear boundary line for Dorinda. Officially announcing her problems is just something she doesn't want to ever do. From the moment Lu was arrested, viewers have consistently said that they didn't think Luann was alcoholic, but that Dorinda, Sonja, and Tinsley might actually be. When Dorinda saw this she stopped drinking for a time, got a personal trainer, and tried to act as if quitting alcohol was just part of her new fitness routine. She'll never admit her substance problems.
The end of August is around when they'd normally begin early contract negotiations and preproduction. They might have told her that she needed to be in rehab for 28 days, they didn't want to lose her for principal photography, and this meant she had to go to rehab in the next month or so. Dorinda probably flipped out and quit.