Protocol is to sweep the floor systematically as long as they do not hear active gunshots. This is because in the time that the witness saw the shooter on floor 2, they could have doubled back to the first floor. It does nobody any good for officers to beeline to the 2nd floor, and get ambushed from behind from a shooter lying in wait. There is also the potential for a secondary shooter.

I'm a cop, and when we went through active shooter training, this is how we learned. The scenario I went through involved a simulated shooting in a small office building. Same things were involved. We made a 4-stack and started sweeping. At the end of a long hallway we heard shots get fired so we began to bypass rooms and casualties, to rush to the source.