The color space follows the document, in the form of an embedded icc profile. It is not set at application level (color settings are just defaults).
Aside from that, CMYK and RGB are generic color modes. What you need to keep an eye on is the color space. That's more specific. Adobe RGB, sRGB, ProPhoto RGB; US Web Coated (SWOP), ISO Coated (ECI), Coated FOGRA39 etc etc.
You can't just "work in CMYK". You need to know which one. Each of those profiles correspond to a very specific printing process: an offset press calibrated to a certain standard, printing on a certain paper using certain inks. There is no "all-purpose" CMYK. Ask your printer.