Starling is warned about the guy behind the fan by Lector.

Maybe he appeared there and Hannibal saw him so warned her before he could shoot? The fan must have blocked the guys angle of sight for shooting. Otherwise it would be strange why the guy wasn't shooting while Hannibal was talking.

The real question is what kind of seasoned FBI agent would shoot at a fan? I mean wouldn't she have used common sense and realized that shooting at a fan that is moving could cause the bullets to come back in her direction and hit her like they did? The only thing I can think of as to how this could potentially be explaine, is that adrenaline took over and she really wasn't thinking clearly just trying to eliminate the target. Either way it was a really stupid move on her part especially since she's supposed to be a seasoned FBI agent.

I'm thinking the guy during the battle was worried about killing clarice, lector and the fan was in the way. He was probably confused and in a hurry so that how clarice was able to get the drop on him.

I just re-watched this movie and I noticed that the guy hand his gun out trying to aim for Clarice, but both the fan and Dr. Lector was in the way. He wasn't able to get a shot off until Clarice move to make her shot. During all of the commotion of everything the guy was probably not thinking straight.