Before Chrono Cross came out, and we knew Lavos being killed wasnt final, I sort of guessed that time got screwed up, and sending Doan and Robo into the gate effectively sent them into inexistence, that time snapped back like a rubber band. As if there was some force that saw that happened, the entity, and had to then erase and rewrite time.
I found it similar to back to the future, with the picture, fading back into correctness, when you altered time, it's not immediate, thus the grandfather paradox. Same reason Marle was there when you ran back into the room (ok that was for show, for our benefit). So...rubber band?
It was like they HAD to go, otherwise some other time paradox would happen?