Wierd, but anyway...

Something to start off with.
Not sure of the implications of using a thread that isn't the event thread
from the event thread.

You should really produce your own SpinnerModel and do something similar in
there.

I'm sure someone will shout me down for this...

import javax.swing.*;

public class Spinner extends JFrame {

static class MySpinner extends JSpinner {

 public void setValue(final Object obj) {
     new Thread(new Runnable() {
         public void run() {
             try {
                 Thread.sleep(333);
             }
             catch(InterruptedException e){
                 e.printStackTrace();
             }
             MySpinner.super.setValue(obj);
         }
     }).start();
 }
}

public Spinner() {
 setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
 JMenuBar bar = new JMenuBar();
 setJMenuBar(bar);
 JMenu menu = new JMenu("File");
 bar.add(menu);
 menu.add(new JMenuItem("Test"));
 getContentPane().add(new MySpinner());
 setVisible(true);
 pack();
}

   public static void main(String[] args) {
    new Spinner();
   }
}