Sometimes the moisture drains when the fans and or compressor is no longer running, we would to know more about your system, it could be a bad valve in the supply to the humidifier causing the water but more information is really needed to provide a positive answer.
Right after I asked this question I realized the blower needed to be running for EAC to have power.
I moved HOT HUM to HOT EAC and now the humidistat will start the blower, which will power on the outlet that powers the humidifier's fan unit. I also unplugged NEUTRAL EAC since I'm no longer using it. Let me know if I did anything stupid here.
I had a similar issue with my Apirlaire humidifier last winter. Turns out the humidstat was bad, not the solenoid like I originally thought.
In mine, I have a red wire from the transfomer to the humidstat. Then a white wire from the humidistat to the solenoid, and white again coming out of the solenoid. This white goes back to the furnace to a door switch (...