The first day I drove my Model S to work was also the first and second time that I experienced the side collision avoidance. The first time, there was a car switching lanes into my 9 o'clock position and the side collision avoidance made a few beeps and steered my car to the right of my lane. The second time was pretty much the same, except from my 3 o'clock position as they were coming up from a freeway on-ramp.
Both times my MS saw the other cars before I even knew what was going on. AP was not enabled and I had my hands on the steering wheel. The car steered to the right/leftmost part of the lane to avoid the perceived threat, but nothing manual steering couldn't overcome (in fact, the first time the alarm went off and the car started steering to the right, I instinctively steered the car right back to the center with just a moderate amount of force...fortunately the car that was in my 9 o'clock position was in a hurry, apparently, and they passed me pretty quickly.)