Fanyo,
I have never heard of this issue before. There is nothing uncommon about the input or output impedance of this version of the Quaverato, so that’s not the issue. My only guess is that it has something to do with the frequency response of the Quaverato. If you have drives or other pedals that are sensitive to the frequency response of the input signal, they may be boosting those particular frequencies more than others. Have you tried changing the order of the pedals in your chain? Most people run modulation effects like the Quaverato toward the end of the pedal chain, partially for this reason…modulation effects often have a tendency to shift the phase of different frequencies. Another thing that might help is to keep a non-true bypass pedal directly after the Quaverato…like a tuner pedal or a buffer pedal or something.
I’m sorry about this issue. I hope you can find a solution that works for you. I’m sorry that I can’t be of more help.
Take care.
-Brach