Cars don't tend to jump sideways all of a sudden (and if they do, then usually by outside force, which tends to be hard to avoid). There's plenty of frames to detect that (note that the view shown is not the only camera, otherwise making a turn safely would be fairly impossible).
Much faster than a human would react. Acutely focused humans generally take at least 1 second to hit the brakes in an emergency. Longer if distracted or tired[1].
There's a fun parlor trick which takes advantage of human reaction time too: place a hundred dollar bill on the table, let the other party place their hand a few inches away, start your hand a foot above theirs; the first person to place their hand on the money wins, and the other party can start moving as soon as you start moving. Turns out you can easily go around their hand and grab the bill before they're able to react.
The distance is beside the point. The amount of time it takes for your brain to parse visual stimuli, then propagate a signal to your arms, and finally for the muscles in your arm to contract will be much slower than a computer parsing a sequence of images and then actuating the steering column. The computer is faster both at understanding it needs to respond and at signaling driving systems to respond.
