Colors are not coming through correctly.

Because pure cyan is very hard to reproduce on screen, CMYK colors are rendered as only rough approximations.  This is because screens are RGB only. The only way to get accurate CMYK colors would be by using color profiles, and as far as I'm aware, supporting color profiles in the browser is somewhere between very hard and impossible.

You will get much better color consistency if you use color-managed RGB colors rather than CMYK.  In fact, if you are going to be printing the result on a printing press, color-managed RGB will generally give better results because RGB has a wider color gamut than printing presses and the color conversion to CMYK will get done using a prepress process using ICC profiles that are optimized for the press.  The one exception to using RGB is if you are using specific CMYK spot colors, such as Pantone.