Works fine for me.. are you sure you're still logged in? Is it perhaps a browser cache issue?
EDIT: Note, that after your expiring setcookie() call (the one where you set the time in the past), the cookies will still be available in the $_COOKIE superglobal, as this is only updated at the beginning of a script's execution; not every time cookie information changes.
EDIT2: For a possible solution, try [man]unset/man'ing the $_COOKIE indeces too:
setcookie("loggedin", "", time()-(36000 * 24));
setcookie("mysite_username", "", time()-(36000 * 24));
unset($_COOKIE['loggedin'], $_COOKIE['mysite_username']);