The tank is not suposed to empty. Only about a third of the tank is supposed to go through the flush valve when you push the handle. That should be about 1.2 gals, and should be enough to make it work.
Perhaps the flapper has been replaced? Or are these the flappers that came with the toilets?
What model Toto do you have? That's important as far as helping you. Just reply to this post with the model number in the tank. That should be enough for us to figure out the rest.