To test, click one of the buttons on the applet to open a dialog window, then navigate away from this page via any means.
The dialog windows should close as the page is navigated away from.
In Safari, if any 'broken' dialog windows are left open, the Safari window will close as well. Also, if this is repeated more than once, or if any more Safari windows are open, quitting the application will warn of closing more than one window, though the count will be incorrect, including the windows which closed.