Why do people still bring up vapor barriers, NOWHERE DOES THE DOE RECOMMEND VAPOR BARRIERS. And they have nothing to do with ice damming. Don't add a mechanical fan either, sounds like fixing the short circuiting airflow did it.
You have heat loss what ever you do. the heat creates the current that draws air and if it's drawing wet worm air into the attic it will further heat the roof. Run your exhaust pipes thru the roof or thru the gable ends with insulated ducts, put in the channels and close the gable vents. The lost heat will still create the air flow but that flow will move the heat along. Venting wet air into the soffit is always a bad idea.
Run your shower with the fan on and go outside and have a look. You believe what you see.