Exporting a vector logo to JPG/TIFF changes colour values

[Ndeetail]

Hello, I'm facing a perplexing problem while exporting a vector graphic (a logo) from illustrator. The document colour profile is CMYK and I'm attempting to export high resolution JPG/TIFF files for print in CMYK. While doing so, I'm noticing the colour values shift a bit. The colour I want my logo to have is the following:

 

But the output in JPG provides different values:

I have no idea why this shift is happening. I've also tried to change the profile to "Don't colour manage this document" from the default "Working CMYK: U.S. Web coated (SWOP) v2" in illustrator. But that doesn't seem to have helped either. What am I doing wrong?!

Thanks in advance!

[Ton Frederiks]

That is how jpeg works, it makes files smaller by averaging and simplifying colors.

You should get a better result with tiff.