I'm still having this problem but I'm noticing it mostly with greens.
Uploaded pic at FT

I can't seem to upload a copy to any internet site that doesn't create the color shift, but the leaf in the bottom right corner should be a darker green to a cooler green gradient, but as you can see it comes out as just a bright green. This file was created in CMYK with colors from the default color palette in AI. Also the rest of the colors are somewhat accurate but have a brighter (not in a good way) tinge to them.
Any AI experts out there know what I am doing wrong? Please!