External links are opened in the default profile which you can change in real time by visiting about:profiles and clicking the "Set as default profile" button. Note that to avoid conflict, only one browser session can make changes to about:profiles at a time.

Alternatively you can add the -no-remote argument to the shortcut to ignore external links, this would require launching from separate day/evening shortcuts for each profile.

Hey zeroknight! Thanks for the answer, but it doesn't solve my problem.

The links open in the personal profile, although the work profile is set as the default one.

I tried switching them, and nothing changes.

Make sure they are not separate installations. Go to about:support in each profile and check that the "Application Binary" values are the same.

The default browser configuration could possibly be specifying a profile which would take precedence. Try re-installing Firefox and re-applying it as the default browser without specifying a profile.

The value for Application Binary is the same for both:

/Applications/Firefox.app/Contents/MacOS/firefox-bin

So, zeroknight was right in the first answer.

I accessed about:profiles from the Work profile, and there this profile was set as Default, although the links opened in the Personal profile.

Then I accessed about:profiles from the Personal profile, where I set the Work profile as Default. Now the links open in the Work profile.

If anyone else encounters this problem, check the about:profiles settings in both profiles.