Photoshop :: Color Shift When Pasting From CMYK To RGB Document

We're creating an image for a client that will eventually be printed 4c process, and we have to use some very specific CMYK values. However, since we need to use certain layer effects, we need to work in RGB. I assumed that since the CMYK values we use are within the RGB gamut, there would be no color shift when copying from a CMYK doc and pasting into an RGB doc, but I'm apprently mistaken.
 
I'm not very familiar with color management, since we don't do any heavy duty color work in house, so this is likely a very rudimentary question: how do I keep colors from shifting when pasting from a CMYK document into an RGB document (which will eventually be converted back to CMYK for print)?