I put white gradient (white to zero) on orange in CMYK-doc and receive Yellow. What does that mean? Visual bug?
Your explanations need some guessing. I guess you try to put the BW gradient to modify underlying orange color. You use blending mode overlay or color burn to do it. Then you have met the following:
This is a CMYK document in Illustrator. Upper stripe has blending mode = normal, lower has blending mode overlay, both are the same white to black gradient. (The result is the same in blending mode Color burn)
Photoshop behaves differently. The next is same stripes in Photoshop:
A big difference! Why?
A long survey revealed a simple truth. There's difference how black is defined in the gradient. By default Photoshop gave to me so called rich black. This results varying CMYK values along the gradient. Illustrator gave C=M=Y=0, K=1. This results to gradient where C=M=Y=0, only K varies.
This is easy to change in Illustrator. Only define the black end of the gradient by yourself, take rich black from the swatches. K-only black can be set with sliders in colors panel (it must be in CMYK mode).
In Photoshop I found a tendency to put automatically rich black in place of K-only black. I haven't found how to switch it OFF.
Another long survey popped up Adobe's PDF specification. There the blending modes were shown as formulas - Adobe's formulas- and also how to convert them to CMYK mode.
Reliable reading the spec needs a person who is a programmer and a mathematician, so I do not repeat the details. I'm not a competent commentator, but as far as I could understand the formulas, in overlay the varying K doesn't affect to the result at all, if K=0 in the bottom shape. Manual calculation also confirmed the constant yellow result.
In Adobe's Photoshop and Illustrator documentation there's no formulas for blending modes, only qualitative descriptions. The complexity of the formulas in the PDF spec is only one possible explanation.