Benjamin Sisko's mother was possessed to ensure he would be born and become the emissary but in the Mirror Universe the wormhole had not been discovered, the prophets had not been met and Sisko was not the emissary. How could there be a mirror Sisko given these facts?
Trying to address this from an in-universe perspective, you are missing 1 crucial fact - when Sarah Sisko was possessed by the "prophets," the wormhole had yet to be discovered in the main universe. The prophet that possessed her left the wormhole to ensure Benjamin Sisko would be born so he could eventually become the emissary (and one of the actions of the emissary was to discover the wormhole).
So there is absolutely no reason to believe that the same thing didn't happen in the mirror universe. The only difference is the mirror universe Ben Sisko never fulfilled his destiny and discovered the wormhole.