It sounds like the white or hot wire is connected to the beginning of the coil and the black wire is hooked to the finish of the coil. This can make your pickup electrically out of phase instead of magnetically out of phase. By carefully reversing the two wires at the pickup will make the beginning of the coil connected to the black wire and the finish of the coil to the white wire. This will also make the coils in phase when used together and eliminate the buzz you get when accidentally touching the pole pieces.

If you decide to reverse the wires at the connections instead of at the pickup it will work, but I like to keep the black or beginning wire grounded on the pickup. You could reverse the magnetic phase on one pickup to make it in phase when used in combination with the other but the poles would still buzz if accidentally touched. Basically the hookup wires had been put on the opposite sides of the coil. This can happen when the pickup is rewound or repaired and the wires are put on wrong.