Fork, I understand people react to the red indicators. I will try to better explain what I see sometimes.
Lets say you're in game and you fling your mouse across your desk. We all have machines capable of producing over 100 FPS in game, so you would see a 360º view of wherever you are on the map. And when people react to being shot (myself in included) there are a few frames where you see the person changing direction. (you can see the scene change from looking infront to looking behind, you see your surroundings)
What I've seen a few times is as follows:
Player1 is engaged in a firefight already, they've already focused on a target. Player2 approaches from the side or behind, outside of player1s feild of view. If the player2 fails to hit player1 in the head right off the bat, player1 is instantly looking right at player2 (crosshair on body). There are no frames of the scene in between from someone doing a quick movement with their mouse.