Illustrator objects (including color) are color managed when the right settings are made in the Color Settings.
You will get options how to habdle a mismatch.
But this does not work for single colors added from the Swatches panel, they are not color managed.
I cannot see why it should not be possible to add a reference to a color profile with a color (swatch) or a document item.
Thanks for sharing your feedback, we have heard this request many times and it’s already in our backlog. We are assessing when we can deliver this feature to our customers.
2 votesNEEDS MORE FEEDBACK · AdminFernando Centurion (Product Manager, Adobe Systems Incorporated) responded
Can you provide details of how to replicate the current scenario?
How are you saving groups of colors?
Are you saving the colors to the Libraries Panel?
Are you using the colors from the Libraries Panel in the new document?
How are you using groups of colors?
See also this report on Process colors becoming Spot colors:
"I am not even touching the subject of Color Managed swatches in CC libraries. "
But I do here:
Looks like a problem with Lab colors.
I tested some other Pantone solid colors added from InDesign to a CC library.
When used in Illustrator, they all become Process colors, 100% Magenta, but keep their Pantone name when added by double clicking the swatch in a CC library.