I don't think there was any specific point where they turned evil; their culture just developed toward violence. Not that ours didn't, of course, but things here got better by the mid-to-late 21st century. I guess that didn't happen in the Mirror Universe.
It started in different points in history for each race. In one of Homer's tales of ancient Greece, Achilles kills King Priam, Khan and the augments won but wiped each other out. Vulcans didn't use logic. Molor won over Kahless, and they didn't use their honor system. Everything is evil and/or opposite after those points.
>>Okay, this is just another alternate universe, albeit a particularly fascinating one, because all of these events came to pass, resulting in the Terran Empire, etc.?