See Case 0189293847.
"Basic RGB" Colour Swatch does not change colour when switching files (tabs) of open files with different Embedded profiles.
If you close down then open illustrator, it will take and then keep the swatch with that profile.

Replication of error.

1. Create .ai file that has the "ProPhoto RGB" assigned profile and save ensuring the ICC profile is embedded
2. Create .ai file that has the "sRGB" assigned profile and save ensuring the ICC profile is embedded

3. Edit>"Colour Settings", and set the Working Space RGB to "ProPhoto RGB"
   Tick on:

   • Profile Mismatches
   • Missing Profiles Press OK

4. Close down Illustrator

5. Restart Illustrator

6. Open up the "ProPhoto RGB" file first,
   then open up the "Basic RGB" swatch panel:
   Swatches Window > from the Menu "Open Swatch Library" > "Default Swatches" > "Basic RGB"

7. Screen grab the "Basic Swatch Menu" and place into MS Office Paint
   You will notice the very saturated Red, Green Cyan and Magenta

8. Open up the "sRGB" file next
   Note that the "Basic RGB" swatch panel does not change colour.
   Screen grab and paste into Paint and compare.

9. Now close down Illustrator and repeat the process,
   but this time open up in the opposite order:
   "sRGB" first
   "ProPhoto" second

You will notice this time that the "Basic RGB" swatch panel is not so saturated,
and now matches the first file opened "sRGB".
switching between panels does not change the colour of the "Basic RGB" swatch panel.
Screen grab the "Basic RGB" swatch panel and paste into paint,
and compare .. you will notice the change of color.

The "Basic RGB" swatch panel should change colour as you switch between files that are open.
It doesn't. This is a bug.

You can change the "Colour Settings" so that the working space profile is "sRGB":
Edit>"Colour Settings", and set the Working Space RGB to "sRGB"
and repeat the stages above and you get the same issue.

You should not have to shut down illustrator, for the swatches panel to pick up the new colours
as you switch between open files on the tab.