Once you have rescued at least 10 of each animal in any one region the Time Machine will appear. Continue to rescue animals until you have at least 10 animals in every habitat in 10 regions to activate the Time Machine for rewind.
When you use the Time Machine, your game is reset back to the beginning with the exception of any discobux, space coins, and decorative items (balls, hats, decor) which are retained. There is a zoo stat for lifetime diamonds trophies which tallies your past diamond trophies across rewinds. You also get access to a new timeless animal each time you rewind. There are 12 timeless animal species in all, 1 for each region.
After you rewind, you cannot rollback to your previous zoo.