How to connect button to joystick?

It would appear that the knob you have is meant for a smaller Joystick like the Parallax Joystick Module they sell at Radio Shack. The first picture shows the Esplora knob on the left next to the Parallax knob on the right-
The Parallax Joystick has a thinner, metal Joystick Rod so the hole is much smaller-