Although the property is set to true, nothing really happens:

   @Override
    public void start(Stage stage) throws Exception {
        stage.setScene(new Scene(new Group(),100f,100f));
        stage.show();
        Stage stage2 = new Stage();
        stage2.setScene(new Scene(new Group(),100f,100f));
        stage2.initOwner(stage);
        stage2.show();
        stage.setIconified(true);
        System.out.println("stage.inconified=" + stage.isIconified() + ", stage2.inconified=" + stage2.isIconified());
    }