The Star Trek: Survival timeline is consistent with the Prime timeline in the television shows and movies until late 2374 and the events of the Deep Space 9 episode 'In the Pale Moonlight.' The divergence begins when Captain Sisko and Elim Garak attempt to bring the Romulans over to the side of the United Federation of Planets.
The Romulans see through the second subterfuge and they renege on the non-aggression treaty to instead side with the Dominion. The tide does not turn in favor of the UFP and its allies, and a bloody war drags on. It destroys countless installations and lives.
In early 2379, staunch allies in the form of the Klingons withdraw from the alliance and all return home to their own space to hunker down and hold out against the Dominion siege. This leaves what remains of Starfleet even weaker, and the war ends with the UFP's surrender toward the end of 2379.
Fearing an outcome such as this, an evacuation was prepared for after the departure of the Klingons. With the Dominion's "mercy," this fleet is gathered together and what remains of the UFP and Starfleet decide to get as far away from the Dominion as they can: they plan to head to the Delta Quadrant to find a new home and a new life.
This is where the story of the USS Minerva takes place.
In the Klingon Empire, Chancellor Martok dies in combat against the Dominion as the imperial fleet keeps more Dominion attacks out of their borders. After internal struggle, Rekta of House Rekta ascends to the chancellorship and leads the Empire against the Dominion.
Many of the houses are not happy with having lost, especially to a woman, and there continues to be internal struggles and potential traitors to the Dominion.
This is where the story of the IKS baH lI bathlh takes place.