Just a theory, as I'm not using Xfce at the moment: I think it uses gvfs for dynamic mounts and I think that makes the device appear only for the current user.
1 - check its permissions - it will probably be mounted under /media with a name based on the device, e.g.
ls -l /media/Travelstar
If you have permissions like drwxr-xr-x it won't be writable by the other user; if drwx------ it won't even be visible to the other user.
You would need to change the mount options for the device ... somewhere in the control panel.
2 - even with this sorted out, the icon may not appear on the other user's desktop ... ie as a file in /home/user/Desktop ... but this doesn't mean it's not accessible