If they knew that they were simply in an alternate timeline, then why were they all so upset that the colony was gone? Why did they need to duplicate the Defiant to maintain it? Why was Kira willing to die to preserve it? Why was she furious with Odo at the end? The whole crux of the episode is that these people either live or die, based on their decision. If they jumped timelines, as you suggest, then what's the problem?