There are 3 strategies employed by the traditional feedback manager, and usually at the same time.
- Limit gain.
- Phase change.
- Frequency shifting. This may vary depending on the HA brand, but for Oticon, if I remember correctly, it’s only a 10 Hz shift, not a whole octave shift. I think an octave shift up doubles the frequency of the pure tone, and conversely halves that frequency on an octave shift down. They only shift everything by 10 Hz to minimize the perception that the music is out of tune.
Nevertheless, you’re correct that this frequency shifting is what is causing the warbling effect. It’s especially more noticeable on pure tones. You hear the shifted note through your HAs, and you hear the natural unshifted note going through the vent in your domes and hitting your ear drums naturally. The 2 are out of sync by 10 Hz, obviously enough sometimes to create the warbling effect due to slightly out-of-sync cancellation spots when the 2 waveforms are combined.