That's the way it's supposed to work, yes. But it gets those profiles from the OS, so if it's the wrong one it's most likely an OS problem.
What happens if you keep the app frame on 1, and drag an image over? It should "snap" when you drop it.
Edit: where are you confirming the profile? Under Color Settings > Monitor RGB? I'm currently using a single monitor setup so I can't check, but I think it just lists the primary profile there in either case.
I have a very useful little app called "DisplayProfile.exe" once made by x-rite. It shows the active profile for whichever screen it's open on. I tried to find it again, but apparently that filename has subsequently been hijacked by some malware, and x-rite doesn't have it on their site anymore. Too bad.