My 1964 LeSabre has a similar feature, though I’m not sure they billed it as a fuel-saving feature. It has a little switch that, when you’re sitting stopped with the engine idling in gear, reduces the transmission fluid pressure and stops the car from creeping forward.
My guess is that your car probably doesn’t actually go into neutral gear, but does something else to reduce the effort needed to turn the transmission. Another thought is that the only way such a feature could concievably save any gas would be if in addition to disengaging the transmission, it reduces the idle speed considerably. If this is the case, perhaps when you actually select neutral, it goes back to the “default” idle speed, which could be the clunk you feel.