Linking a CMYK Illustrator .AI file in an CMYK InDesign imports colors as RGB
When importing a CMYK Illustrator file in a CMYK InDesign document it converts the colors to RGB.
This happens in InDesign 2020, 15.1.3. Not certain how long this has been an issue. We recently had to change our links in many files from .AI to EPS / PDF files.
Be sure in InDesign, in Edit / Transparency Blend Space / Document CMYK is selected. Also be sure your imported AI files are in same color space as InDesign, or with no color space assigned (if they differ, you get rich black from pure black in imported AI, also all colors with unwanted changes).