Continuity mistake: In the opening, the camera zooms in on an eye that is a very light greyish blue. The camera then cuts to a man lying on the floor. The implication is that it's this man's eye. However, the man's eyes are brown.
Continuity mistake: Throughout the movie they are told to suck on the buttons from their shirts. In one scene, once Holloway climbs into the next room, Quentin is sucking on his button. He immediately speaks to Worth, muddling some words because of the button in his mouth. All of a sudden, the button disappears from his mouth and is in his hand again, and he then puts it back into his mouth.
Continuity mistake: Throughout the movie, Leaven's glasses have a crack in them that appears and disappears.
Continuity mistake: The blood patterns on Worth's face periodically change throughout the rest of the movie after Quentin beats him with the shoe.
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.