The animated graphic of the Terran Empire's logo seen in Enterprise shows Earth spinning in the opposite direction, meaning in the MU the sun would rise in the west and set in the east. For awhile, it was my "hed canon" that the difference in humanity between the two universes was triggered by cavemen travelling in the direction of the sun.When did it begin? If the mirror universe split off the prime universe as a result of something the prime universe people did, the future mirror universe inhabitants would inherit the name "mirror universe" from their prime predecessors.
The matter gets muddied in Disco, where their animated graphic of the Terran Empire's logo does show Earth spinning in the correct direction, but the continents are inverted, meaning the east coast is now the west coast, and the west coast is now east.
Regardless, both depictions make it clear Earth was always different in the Mirror Universe than in the Prime.