For New Vegas at least, I had to copy the FalloutCustom.ini into the profile folders before it would switch them when changing profiles.
By default only FalloutPrefs.ini and Fallout.ini are profile dependent with Vortex.
Profiles are in C:\Users\*YourUserName\AppData\Roaming\Vortex\*GameFolder\profiles
These are the default locations I am pretty sure, so if you installed them elsewhere you're probably just looking for ...\Vortex\*GameFolder\profiles
It does not does?(it's weird, just update it in the profile folder when the profile isn't active) update them like the other ini files when changing them in C:\Users\*YourUserName\Documents\my games\*GameFolder (If it updates others at all. I didn't test other ini files)