The two worlds run parallel to each other. So when the birds discover time machines and go back in time to avert their Crapsack World, so do the humans of the future to avoid their Crapsack World. And the worlds in the past they go to are actually each other's worlds. So in what was formerly Domain, humans started to populate the earth, and in what was formerly the human world, animals start to populate the earth. We've already seen what caused the human world to go crapsack and the birds to find the time machine in canon. What caused Domain to go to hell was the emergence of naturally born humans in Domain. Those two, or some descendants of theirs, will be the ones to find the time machine and go back in time.