The following information may be of use to you.
I have a web page with 12 frames. On each frame there is an instance of a Java applet. Each instance uses a different port.
Each instance has a menu that is activated by moving the mouse on top of the applet.
Sometimes, the same image appears on two different frames, which is the same problem you have. Moreover, when that happens, moving the mouse on top of one image activates the menu on the second image.
The first conclusion is that the phenomenon has little to do with the applet itself, although it could be triggered by some java feature used in both cases.
Second, I have found that usually, after refreshing the applets two or three times, the phenomenon disappears.
I hope this helps, and if you find anything, please email me.