FULL PRODUCT VERSION :
java version " 1.7.0_21 "
Java(TM) SE Runtime Environment (build 1.7.0_21-b12)
Java HotSpot(TM) 64-Bit Server VM (build 23.21-b01, mixed mode)

ADDITIONAL OS VERSION INFORMATION :
Mac OS X 10.8.0

EXTRA RELEVANT SYSTEM CONFIGURATION :
iMac8,1
2GB RAM

A DESCRIPTION OF THE PROBLEM :
When the user right-clicks on the installed TrayIcon, the PopupMenu that was passed to the TrayIcon constructor is not displayed. The PopupMenu is displayed only when the user left-clicks the TrayIcon.

STEPS TO FOLLOW TO REPRODUCE THE PROBLEM :
1.) Create a TrayIcon with an associated PopupMenu
2.) Insert TrayIcon into SystemTray instance
3.) Attempt to right-click the displayed TrayIcon

EXPECTED VERSUS ACTUAL BEHAVIOR :
EXPECTED -
The user expects the PopupMenu to be displayed whenever they right *or* left click the TrayIcon, just as other icons in the notification area do on Mac OS X.
ACTUAL -
The PopupMenu was not displayed when the user right-clicked the TrayIcon. If the user right-clicks other non-Java icons in the notification area on Mac OS X, their associated popup menu's are displayed.

REPRODUCIBILITY :
This bug can be reproduced always.

---------- BEGIN SOURCE ----------
import java.awt.AWTEvent;
import java.awt.MenuItem;
import java.awt.PopupMenu;
import java.awt.SystemTray;
import java.awt.Toolkit;
import java.awt.TrayIcon;
import java.awt.event.AWTEventListener;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;
import java.awt.event.MouseEvent;
import java.awt.event.MouseListener;
import javax.swing.ImageIcon;

public class TrayTest
{
  
  public static void main(String[] args ) throws Exception
  {
    MenuItem mi1 = new MenuItem( " Test Action 1 " );
    MenuItem mi2 = new MenuItem( " Test Action 2 " );
    MenuItem mi3 = new MenuItem( " Exit " );
    
    mi1.addActionListener( new ActionListener()
    {
      @Override
      public void actionPerformed( ActionEvent e )
      {
        System.out.println( " Test Action 1 - actionPerformed() " );
      }
    });
    
    mi2.addActionListener( new ActionListener()
    {
      @Override
      public void actionPerformed( ActionEvent e )
      {
        System.out.println( " Test action 2 - actionPerformed() " );
      }
    });
    
    mi3.addActionListener( new ActionListener()
    {
      @Override
      public void actionPerformed( ActionEvent e )
      {
        System.exit( 0 );
      }
    });
    
    PopupMenu pm = new PopupMenu();
    pm.add( mi1 );
    pm.add( mi2 );
    pm.addSeparator();
    pm.add( mi3 );
    
    ImageIcon icon = new ImageIcon( " ./icon.png " );
    TrayIcon trayIcon = new TrayIcon( icon.getImage(), " Test System Tray " , pm );
    SystemTray.getSystemTray().add( trayIcon );
  }
}
---------- END SOURCE ----------

CUSTOMER SUBMITTED WORKAROUND :
You can install a custom MouseListener on the TrayIcon and trigger the PopupMenu to be displayed via the following example:

import java.awt.AWTEvent;
import java.awt.MenuItem;
import java.awt.PopupMenu;
import java.awt.SystemTray;
import java.awt.Toolkit;
import java.awt.TrayIcon;
import java.awt.event.AWTEventListener;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;
import java.awt.event.MouseEvent;
import java.awt.event.MouseListener;
import javax.swing.ImageIcon;

public class TrayTest
{
  
  public static void main(String[] args ) throws Exception
  {
    MenuItem mi1 = new MenuItem( " Test Action 1 " );
    MenuItem mi2 = new MenuItem( " Test Action 2 " );
    MenuItem mi3 = new MenuItem( " Exit " );
    
    mi1.addActionListener( new ActionListener()
    {
      @Override
      public void actionPerformed( ActionEvent e )
      {
        System.out.println( " Test Action 1 - actionPerformed() " );
      }
    });
    
    mi2.addActionListener( new ActionListener()
    {
      @Override
      public void actionPerformed( ActionEvent e )
      {
        System.out.println( " Test action 2 - actionPerformed() " );
      }
    });
    
    mi3.addActionListener( new ActionListener()
    {
      @Override
      public void actionPerformed( ActionEvent e )
      {
        System.exit( 0 );
      }
    });
    
    PopupMenu pm = new PopupMenu();
    pm.add( mi1 );
    pm.add( mi2 );
    pm.addSeparator();
    pm.add( mi3 );
    
    ImageIcon icon = new ImageIcon( " ./icon.png " );
    final TrayIcon trayIcon = new TrayIcon( icon.getImage(), " Test System Tray " , pm );
    
    trayIcon.addMouseListener( new MouseListener()
    {

      @Override
      public void mouseClicked( MouseEvent e )
      {
        if ( e.getButton() == MouseEvent.BUTTON3 )
        {
          JFrame blank = new JFrame();
          blank.setUndecorated( true );
          blank.setVisible( true );
          blank.add( trayIcon.getPopupMenu() );
          trayIcon.getPopupMenu().show( blank, e.getX(), e.getY() );
        }
      }

      @Override
      public void mousePressed( MouseEvent e )
      {
      }

      @Override
      public void mouseReleased( MouseEvent e )
      {
      }

      @Override
      public void mouseEntered( MouseEvent e )
      {
      }

      @Override
      public void mouseExited( MouseEvent e )
      {
      }
      
    });
    SystemTray.getSystemTray().add( trayIcon );
  }
}