The mirror universe is a whole other "entity" of it's own, and not the same as the Prime/Alternate timelines.
The alternate timeline in question, basically follows the same pattern that the Prime timeline would've taken, if the Enterprise-E and the Borg weren't involved in First Contact, and if Nero hadn't destroyed the USS Kelvin.
The mirror universe on the other hand, is basically our prime timeline turned 180 degrees. Where the good guys suddenly are evil, and the bad guys aren't so bad anymore.