On Windows OS all popups are get hidden when you press Alt+Tab,
I think it should happen on GTK as well

This bug is very visible with the JTrayIcon draft implementation

Expected:
You press Alt+Tab and popups are closed

Actual:
Popups stay open

To check it use the following test:

import javax.swing.*;

public class PopupTest {

    private static void createGui() {
        final JFrame frame = new JFrame();
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);

        JPopupMenu menu = new JPopupMenu("Menu");
        menu.add(new JMenuItem("MenuItem"));
        menu.add(new JMenuItem("MenuItem"));
        menu.add(new JMenuItem("MenuItem"));
        menu.add(new JMenuItem("MenuItem"));
        menu.add(new JMenuItem("MenuItem"));

        JPanel panel = new JPanel();
        panel.setComponentPopupMenu(menu);
        frame.add(panel);

        frame.setSize(200, 200);
        frame.setLocationRelativeTo(null);
        frame.setVisible(true);
    }

    public static void main(String[] args) throws Exception {
        SwingUtilities.invokeLater(new Runnable() {
            public void run() {
                PopupTest.createGui();
            }
        });
    }
}