With most japanese joysticks (unsure about the ultimarc though I've heard it's made by sanwa) you simply get a flathead screwdriver to hold the bottom bit of the joystick, and turn the balltop as hard as you can. You can reverse turn to lossen the balltop. All sanwa and seimitsu joysticks I've seen are tightened this way. I've yet to see any balltop come loose after doing this.
Hope this helps...