My opinion:
What you are likely observing is humm induced oscillation or parasitic, that for this part of your circuit has become "the optimized bandwidth and/or the maximum gain within a frequency range" created by the pot's divider network which is frequency dependant through this range or setting. I hope I'm saying this clearly enough to get my thought accross?
Also, when you're using pots on the faceplate, their location is at a (sometimes great) distance away from the circuit board & components which then extends grid and plate wiring which then potentially creates issues where the wiring can pickup stray currents and induced noise much easier (especially if not shielded w/ longer runs). This will also affect to a greater extent or sensitivity to what I said in the earlier paragraph.
So there's several factors to consider regarding the pot's role for the given part of the circuit you're using it in. This is where layout design and lead dress becomes very important to minimize any of these effects. It can be affected by tone control settings at times but not always. Wiring also has capacitance. Capacitance together with pot's resistances create varying high & low pass circuits which create inherent varying frequency responses. Coupled with the tubes gain and frequency production and you can see why this phenomenon occurs. The controls of highest probability (or noticeable) with this are the gain and volume pots since the frequency dependant parts of the circuits created by these resistor/capacitor networks are amplified directly by them until heard or they negatively affect the circuit response. But this can also be out of our auditory range and show up as other symptoms like a decrease in or very little sustain for example since the note's upper frequencies (harmonics) are being canceled out.
You then have other parts of the circuit/amplifier which can affect the overall performance and/or earlier stages via coupling, induction, or reactances such as negative feedback networks, proximity to heater, B+, plate, cathode, and output transormer wiring.