Parallel universes do not require a branch. In premise, they simply exist alongside one another throughout their histories - you know, "parallel" - but events in each take different turns.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.
This concept used to be part of sf's stock-in-trade, but the notion of branching quantum realities has so supplanted it in the popular imagination that it gets muddled and eventually, I expect, folded in. Sort of how Khan transformed from a eugenically-bred human to a "product of genetic engineering"