The "Effects of Controls" exercise is demonstrated by holding all controls in a fixed position, while the one that is to be demonstrated gets moved.
The instructor is not correcting for any primary or secondary effects, just holding everything else fixed while the poor little unstable beast gyrates itself into an ever-worsening situation. Hence the description of "stick-fixed instability".
In real life, Bloggs feeds in some pedal to achieve some aim, and he has to feed in all the other controls to some extent to keep things the way he wants them.
And as far as gyroscopes go, helicopters don't. It is merely a simple and understandable way of describing some things that happen to a helicopter. But gyroscopic, it ain't. Gurgle up some of Nick Lappos' posts from years ago, including one called "Helicopter urban myths."