What if the divergence point is City On The Edge Of Forever?
Honestly the whole alternate timeline thing was just a contrived way not to piss off fans by claiming to wipe out all the events of the show they know and love. But you could say that Spock came in the same timeline because he was caught in the temporal wake or whatever, same reason in First Contact the Enterprise E wasn't erased from history. Or maybe 'Temporal Shielding' was immediately installed on every ship in the fleet after Voyager got back. Make up your own reason. Maybe when Biff Tanen came back to 2015 from 1955 and wound up in his original timeline he created a rift in spacetime that Spock fell through.
And there has to be more going on between these two worlds than just to be alternate timelines of each other. Otherwise, why would almost the exact same people exist in both timelines regardless of events being completely different? Maybe since space, time and thought are all one, the MU was created by our dark suppressed passions, so there are corresponding versions of us who act out on all our suppressed violent urges. Or maybe the Prophets created the MU to help Sisko let go of Jennifer. Whatever, the explanation you make up will probably make more sense than the official one if it existed.