Just swap the connections to the thick black primary coil. Take the white wire and the green wire and connect them to the opposite ends of the black coil.
A simple oscillator like that works because there are two signal inversions, one is in the transistor itself and one is between the primary and secondary winding of the Tesla coil. If one of the windings is backwards you do not get the second inversion and it fails to oscillate. You could reverse the connections to the secondary instead of the primary to get the same effect but that would be hard and dangerous to implement!
Brian.