Could be a few things causing this. You will have to do some investigating with a volt meter to find the problem.
For starters, I would suggest disconnecting the contactor relay coil power and see if it continues to do this.
If so, then you have a bad contactor. If not, then you have erroneous power coming from the air handler controls, up to and including the thermostat. With the coil wires disconnected, notice to see if the fan continues to cycle or if you have 24VAC coming in, over the coil wires. From there, you will have to fall back to the thermostat and disconnect the red wire from the thermostat and see if the fan still acts up.
How do you know that the fan in not just cycling versus coming back on after the system shuts down?
