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I'm sure you did the right thing. If you saw it going amber and it just turned to red as you went through, that's fine. You said there was a car behind you - there's no point in doing an emergency stop and making the car behind you crash into you! (Though that would technically be his fault anyway - he should have enough space behind you to stop, but stil...). If you're really close to the lights when they turn to red, it's far better just to go through when they're on red. Slamming the brakes on to make a red light isn't really great. Besides, the other sets of lights always have a slight time delay on them to give people chance to get through if they have to. Your dad didn't make a fuss about it, and he must have been driving for a while... just try not to do it when you take your test!