Uh, no, Cardassians were being slaughtered left and right for the Dominion, was it half a million at one go at one point? and they were just a diversion. There was no partnership of any kind. Cardassians were dirt to the Dominion, who were giving away territory of theirs to the Breen. Cardassia was just considered a platform to launch attacks from. Imagine being conquered and then willingly fighting for your conquerors like sheep...
The Cardassians were only slaughtered prematurely because of the civilian rebellion. The Dominion were favoring the Breen because they see the bigger picture. The Cardies were there for territory, the breen were there for weapons. They were going to exterminate both races once they had the AQ.
Septimus III occurred before the civilian rebellion, and even before Damar rebelled--in fact, it was the event that set Damar off. So I think it's fair to say the slaughter, or a strong foreshadowing of it, had already started.