Bathroom Fan Leaking/Dripping
You have a roof leak that is dripping either directly onto the fan assembly or onto or into the vent tubing. Probably the leak is around a roof penetration, but we had one due to a defect in the roof decking right above the fan. Water dripped onto the fan assembly, through it, and into the bathroom.

EDIT
Another possibility is condensation of water in the tubing connected to the outlet of the fan. The tubing is in the cold attic and so water vapor will condense on the walls of the tubing conducting the exhausted air to the outside. If there is a lot of condensate in the tubing when the fan is turned off, and if the routing of the tubing is level and upward then this would drain down into the fan assembly unless there is a drain to catch it and conduct it away.