Finally found the fix:
- Go to your Java Contro Panel (i.e., "Configure Java" shortcut).
- Go to "Security" tab
- On the bottom, click "Edit Site List..."
- Add the URL of your VPN without any path, e.g.: https://www.example.com
- Click okay.
When you're done, your security tab should look something like this:
Hope this helps. Got to the solution via Juniper's KB.