In almost all cases, this is because the headphones that you have are stereo headphones whereas the signal coming out of the headphone output of a Wurlitzer piano is mono. This means that (usually) only the left (tip) side of the headphones will be heard as there is no collection to the right (ring).
Solution
The solution is to purchase a mono jack adapter so both sides of the signal come out through both ears of the headphones. As the output signal from a Wurlitzer is mono, you will hear the same signal in both ears like any other mono instrument.
Mono vs Stereo:
On some Wurlitzers, some technicians and enthusiasts have rewired the headphone output so that it a stereo signal. Whilst this is more complicated then simply using a mono jack adapter, it means that stereo jack adapters will work normally. However using a mono jack adapter with the stock amplifier can cause issues due to shorting of the connections.
This is because the speakers are bypassed when the headphone socket is engaged and a ceramic resistor is routed instead. In a stereo connection, the speakers are bypassed and the load of the amplifier is not sent to the resistor. This can cause a backup of current that can cause problems for the amp. So long story short, always use a stereo jack adapter with a stereo headphone output.
