I think this is a form of mach-banding, which is an optical illusion where changes in luminance are enhanced by the visual system, causing the appearance of bright or dark bands which are not actually present in the image. Typically these are seen on the boundary between two distinct areas, but in the case here I believe it is the sharp discontinuity in the gradients being observed.
Here are some images to demonstrate the issue:
This first image is calculated in software, and consists of three circles each drawn with a radial linear gradient. Mach-band effects should be visible at the edges of the overlap between circles, as these are the points where the gradient sharply changes.
This second image is exactly the same calculation, but instead of being linear along the radius, the gradient is mapped to a curve (I used the first hermite basis function). The bands should almost entirely have disappeared:
As to why this affects a colourised image more, I'm not sure it does. I think in the case above, perhaps there is additional banding caused by the colourisation effectively being a palette lookup, resulting in additional banding.
I performed roughly the same colourisation locally, also simply mapping a palette, and the effect is similar:
Fixing this using QT's linear gradients is probably non-trivial (you could try adding a lot more control points to the gradient, but you'll have to add quite a few...), but calculating such an image in software is not hard. You could also consider some other post-processing effects, such as adding a blur, and/or adding noise. Anything breaking the discontinuity in the gradient would likely help.