Well done for noticing this - I know I didn't notice it during my trial lesson, and as my flying advanced I started learning about this kind of effect, and wondering why I didn't see the nose dropping when playing with the rudder on my trial lesson!
I'm not in a position to say that Mad Scientist is wrong, but I'd always thought that it was much simpler than he makes out. Yaw induces roll - the reason for this is that the outside wing is going faster, and so produces more lift. After rolling, the aircraft is banked, so the lift from the wings is no longer directed upwards - there's only an element of it which is pointing upwards. Therefore, you need to increase the lift in order to avoid loosing height. The normal way of doing this is to apply back pressure.
Or, alternatively, your instructor may also have been using ailerons to prevent the aircraft from rolling. In this case, the lift would still be directed upwards because the aircraft wouldn't be banked. However, you'd now be skidding through the air - the aircraft is not as streamlined as it is in normal, balanced flight. This would add extra drag, and slow the aircraft down - and the reduced speed woul reduce the amount of lift the wings produce. Again, this can be compensated for by back-pressure.
I don't think Mad Scientist is right when he says: "The instructor was presumably pulling back on the yoke to maintain your airspeed". I suspect the airspeed was lower than in straight+level flight while you were doing these exercises, and the instructor was actually maintaining altitude.
Did your instructor really not have time to explain? Or did he prefer to talk about this later on when you look at secondary effects of controls in more detail?
Anyway, glad you enjoyed the experience!
FFF
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