I have also faced strange logout behavior while trying to implement private post / private page.
In the few words, I wanted that some posts / pages are hidden from unauthenticated users and used Identity.isAuthenticated for checking .
Debugging isAuthenticated indicated returned true, although FormsAuthentication.SignOut() was called line before ???,
Please Google ".net forms signout isAuthenticated" for more details.
This behavior is not BE related and in my experience it is not IE specific ( as I do not use IE ).
It seems that .NET SignOut method closes a session, but does not delete a cookie and browsers in such case cache the state.
Suggested solution is to expire cookie after FormsAuthentication.SignOut();
Response.Cookies[FormsAuthentication.FormsCookieName].Expires = DateTime.Now.AddYears(-1);
Personally, I did not have success with cookie expiration code, probably because I did not have time to analyze BE cookies.