Unless you want some nasty surprises, NEVER USE THE INDESIGN COLOR PICKER that pops up when you double-click a color box in the toolbox. If you open it accidentally, be very quiet and carefully click the cancel button.
The InDesign color picker operates only in the RGB color space, as a consequence when it works with a color it must translate that color into RGB if it isn't already. In many, if not most cases, there is no exact RGB formula for your color, so the definition is changed to the nearest equivalent in RGB. Upon exit, this value is used to convert the color back into CMYK unless the color was defined in RGB to start.
While there is also a set of fields in the color picker for defining CMYK, these are still tied to the RGB values, and if you type values that have no RGB equivalent they will be converted to the nearest RGB value and then back into CMYK on exit, only you won't see it happening.
What does this mean in real life? It means that grays created from just black ink get converted into rich colors made from four inks and any spot color gets the same treatment. It also means that a process color is likely to be reformulated and shifted due to compound rounding errors in the CMYK to RGB to CMYK round trip. In other words, anything but an RGB color will become 4-color process, and the wrong one to boot.
For defining and editing colors you should stick to using the color or swatches palettes.
Peter