The program does not select the profile of the monitor it's currently on for various reasons. As a workaround, you can create a shortcut with command-line options specifying the monitor to start on, and the ICC profile to use.
The options to start on monitor 2 and use an installed profile named, say, "profile_for_monitor2.icc" would be: -m:2 -icc:profile_for_monitor2.icc
The command-line in the shortcut would look like this (the -k starts the program in full screen mode):
"C:\Program Files\FastPictureViewer\FastPictureViewer.exe" -m:2 -icc:"Some Installed Profile.icm" -k
Use quotes if the profile name contains blanks. You could create two shortcuts, one per monitor, with the appropriate profile selected in each one. It's not exactly automatic but still more confortable than changing the profile in the options.
Existing command-line switches are described in the FAQ:http://www.fastpictureviewer.com/faq/#cmdline