Is it time to start calling out bad cyclists?

Thanks for the sketch. There really shouldn't be any variability in whether the green right-turn arrow is shown. Arrangements like the ones at this junction used to be more common, but have mostly been replaced with split-phase arrangements now, I think. The only one I use regularly is that at the junction of Newington Green Road, Ball's Pond Road, Essex Road, and St Paul's Road, and there definitely isn't any variability there.

If you have time, the following would be a good exercise. Leave ten minutes early tomorrow and stop at the junction and observe it for a while. This may sound boring and a bit trainspotterish, but in this case it should help you process what happened a little. (It is generally a good thing to do when you're getting used to a new route and aren't sure how the junctions work. It doesn't take long and prepares you for riding through it properly. There are usually only a couple of places on people's commutes that cause them difficulty at first.)

Wait for a while at each of the corners of the junction. Walk your bike across the pedestrian crossings and perhaps wait on the splitter islands if you want. Look at the traffic signal phases and driver behaviour. Note any instances of conflict. There may not be any need to do this in your case to understand the junction better, as perhaps with the exception of the arrangements you question you probably already do, but it may just be a good way of taking stock. Obviously, you'll want to pay particular attention to whether the right-turn arrow does come on in a variable way. (I doubt it, and like the others above I think the driver probably ran the red light.)