I've used LaBellas and Pyramids on several basses, from several string sets in multiple gauges. Am 99% sure it is not operator error (the twisting thing) but I have done some stupid things in my life. 
Others have observed the same. Some even claim to be able to hear it in some of McCartney's recordings.
GHS (no affiliation) claims to have a way to reduce the effect. It seems to work though I can still hear a slight difference even in the GHS (but nothing like in the Pyramids or LaBellas).
I had a set of Jamerson 1954's a few years ago and did not have the issue with those. I suspect the reason is that the A string was massive and closer in size to the E string vs the lighter sets.
Others have observed the same. Some even claim to be able to hear it in some of McCartney's recordings.
GHS (no affiliation) claims to have a way to reduce the effect. It seems to work though I can still hear a slight difference even in the GHS (but nothing like in the Pyramids or LaBellas).
I had a set of Jamerson 1954's a few years ago and did not have the issue with those. I suspect the reason is that the A string was massive and closer in size to the E string vs the lighter sets.