Just FYI: It's redirecting to the user's profile as visible by the other users of the site. So if you made a change to your profile, you can immediately see the effect it has on your profile.
The redirect is in usersettings.php, at the end of function saveuser. You could replace the COM_refresh call with the message you want (but you'd have to display the site header and footer yourself, too).
bye, Dirk