Those aren't leaf joysticks, they are microswitch joysticks. The microswitches have an actuator on them, but they are certainly not leafs.
The "metal ring," if I understand what youa re saying, is the E-Clip, and has nothing to do with the pressing of the switches. It has that opening so it can be slid off and on the shaft. Usually all you might have to do is adjust the actuators (long metal pieces coming out of the Cherry microswitches) until you get contact when the joystick is moved.