At the end of Justice League-Crisis of Two Earths, Owlman and Batman end their fight with Owlman the loser, and on a different Earth than the "Prime" with his super bomb. Before it explodes, he says "it doesn't matter", as, during the film, each outcome we encounter creates an alternate reality. By that logic, wouldn't there have existed another Owlman who actually succeeds in destroying reality?
The device that transfers passengers to other universes appears to be an exception that violates the otherwise-canon rule that any change and decision creates a new universe. It really kind of has to be from a narrative perspective, because otherwise Owlman's scheme is meaningless. If he could only travel to a copy of Earth Prime, then destroying that copy he just made serves no purpose. The Earth Prime that all the other Earths came from would still exist, and so would the Earths that stemmed from it.
As such, the rule that an alternate universe Batman would have not stopped him and he therefore would have succeeded does not apply.
But there is a lot of suspension of disbelief required with the entire concept. For example, Owlman brings up Batman's choice to go through the portal himself instead of sending Superman. He doesn't seem to realize it, but this would imply that another Batman chose to send Superman instead, and likely that yet another Batman chose to send the Flash, Green Lantern, Wonder Woman or Martian Manhunter. If we assume that they actually are traveling to the same Earth Prime, then each of those characters should have arrived to stop Owlman.
Another example is to consider that Batman and Owlman's decisions in their battle and conversation on Earth Prime (do I punch or use a gadget? how do I respond to what he just said?) would have created new universes as well, and in some of those, Owlman would have won and destroyed that copy of Earth Prime, though this would not affect the Earth they came from.
A third example is that Owlman actually does appear to consider using the device to transport either himself or the bomb elsewhere after being transported to the barren ice Earth before deciding that it doesn't matter. Another Owlman likely would have transported the bomb back to Earth Prime. Another Batman wouldn't have left the device with Owlman at all. Yet another Batman would have defeated Owlman and then detonated the bomb himself, for no apparent reason.
In short, you're simply expected to suspend your disbelief and accept that the universe was not destroyed, as a result of Batman's victory over Owlman.
The bomb Owlman wanted to detonate would have destroyed all realities, not just the one Owlman resides in, but also the one where the Justice League hails from. Seeing as that the JL universe still exists, it means that no other Owlman was able to detonate the bomb.
Owlman is a firm believer in determinism and that free will is an illusion. His bomb was an attempt to exert his free will on a universe that he believes doesn't respect it, when that fails he just smiles and says "it doesn't matter". He has come to the conclusion that his attempt was futile, that decisions don't matter in the end, and the universe is on rails and will continue on its course regardless of what individuals try.
Despite that this version of the Owlman failed to achieve the Earth Prime destruction the mere fact that he wanted to achieve this purpose implies that there are another version of himself that sooner or later will successfully destroy Earth Prime and any other universe along with it. So yes maybe it would take some time and that explains why JL still exist by the end of the movie.