My first guess would be that you connected the wires to the "normally CLOSED" tabs on the joystick switches, not the "normally OPEN" ones.
There are three tabs on each switch on the buttons and joystick.
One of these is ground (usually the one off by itself).
The other two should be marked NC and NO on the switch somewhere.
You want the two wires going from the joystick to the gamepad hack to be hooked to the NO tab and the ground tab.
The NO tab only sends a signal when the button (or joystick) is pressed.
The NC tab sends a signal only when the button is NOT pressed.