Power supply:
Ground - GND from Teensy (power-rail as described in the PDF attached)
+3.3V - 3.3V from Teensy (power-rail as described in the PDF attached)

Joystick 1:
VRx - Pin 23/A9 (horizontal control)
VRy - Pin 22/A8 (vertical control)
SW - Pin 01 (switch when joystick is pressed down)
+5V - +3.3 V (no worries, 3.3V works too) applicable to all joysticks!
GND - Ground (we found common ground!) applicable to all joysticks!

Joystick 2:
VRx - Pin 21/A7 (horizontal control)
VRy - Pin 20/A6 (vertical control)
SW - Pin 02 (switch when joystick is pressed down)

Joystick 3:
VRx - Pin 19/A5 (horizontal control)
VRy - Pin 18/A4 (vertical control)
SW - Pin 03 (switch when joystick is pressed down)

Joystick 4:
VRx - Pin 17/A3 (horizontal control)
VRy - Pin 16/A2 (vertical control)
SW - Pin 04 (switch when joystick is pressed down)

Control Panel:
STB - Pin 15 (Strobe for TM1638 chip)
CLK - Pin 14 (Clock for TM1638 chip)
DIO - Pin 13 (Digital I/O for TM1638 chip)
VCC - +3.3 V (GND from Teensy via power-rail)
GND - Ground (3.3V from Teensy via power-rail)

More details on this, as well as how to build the device, get the software running on the
Teensy, how to operate the device and much more - please refer to the PDF attached.