Condensation though vent
I call it the “coke bottle effect”. It’s what happens when you take a coke bottle out of the refrigerator. The cold bottle will produce condensation when it meets with the warm room air.

In your case, the warm (probably moist) air from your bathroom is vented up to the cooler outside air. When the two meet and you reach the Dew Point, condensation is created by turning the warm moist air back to a liquid and runs down into your house. 

One way of solving this problem is to insulate the duct and install a backdraft damper at the roof that seals the vent pipe. 

When you installed the ceiling fan it probably came with a backdraft damper. This keeps all the air in the vent pipe at the OUTSIDE temperature. You want the air in the vent pipe kept at your INDOOR temperature. 

I suspect you live in a cooler climate.