When you choose a different profile in the Firefox Profile Switcher menu, it opens a new instance of Firefox with the new profile. The add-on experience will be very familiar if you've used Chromium's profile management features.

If you're trying to create a shortcut to Firefox that launches a profile other than the one you've selected as the default, the instructions for Linux and Windows are here:

https://kb.mozillazine.org/Shortcut_to_a_specific_profile

This is not necessary to use the profile feature, but some people prefer to launch profiles from shortcuts instead of a menu.