I was thinking about this yesterday, when dh and I were out in the car. I think that, when I am driving, I am aware of traffic lights in the distance, and on a subconscious level, I notice how long they have been red or green, on the basis that, the longer they have been that colour, the more likely they are to change. I suspect most drivers do the same.
It is particularly important when you are approaching a green light that is, as a previous poster called it, 'stale' - ie. it's been green for some time and is therefore likely to change to amber. In that situation, I come off the accelerator so the car starts to slow down, and I am ready to decelerate further and stop if it goes amber. And the amount I decelerate is dictated by traffic conditions and whatever's going on in my car - if I've got the dogs in the boot, I tend to drive a bit more gently, so as not to throw them round, and I would decelerate a bit more coming up to some traffic lights that I thought were due to go amber, in order to avoid a sudden stop that might make them uncomfortable.
TBW's dh had an even better reason to want to drive gently - I think he was very sensible to do so - but in that case, he should have been hyper-aware of lights that might be about to change, and he should have left a bigger braking distance between himself and the car in front, coming up to the lights, so he would have enough time to stop without sudden braking if the car in front did an emergency stop.
That said, as the stop board does constitute the stop line, at temporary traffic lights, I would not have expected a car ahead of me, that had gone past the board on green, where there was nothing else going on on the road that might require it, to do an emergency stop. But I would hope to be paying enough attention, and to have enough of a stopping distance, to be able to stop without touching the other car. If I did, it would be my fault for misjudging my speed, my braking or my braking distance.