Revealing mistake: When they get Renn back into the room after he has been shot in the face with something acid-like, the smoke comes from behind his head. Not his face.
Revealing mistake: When Kazan lowers himself into the blue sound-activated room that is rigged with metal spikes, the set cube wobbles from left to right, spoiling the illusion that the cube is made out of solid metal.
Answer: It's established that sound travels throughout the structure reasonably well. Also, they didn't travel relatively far, even with the rooms shifting.
Actually, considering the distance that they travelled and the injuries he sustained, Quentin would have had extreme difficulty catching up. It looks like the 3 travelled upwards at least 12 cubes, meaning Quentin would have had to climb up each one with the chance that any of the rooms could be trapped fast enough to catch up to them with enough strength left over to kill Leaven.
Adrenaline is an extremely driving force, so I'd still consider it entirely possible it happened that way.