If your 1966
Safair's system is simular to my 1968
Tradewind, and I bet it is, the fresh water system was factory designed to allowed you to hook up to city water, open a valve, and fill up your fresh water tank. Perhaps this valve is partly open or has failed.
I discovered this while camping, hooked up to campground water, and found water overflowing from the fresh water tank. I traced the "city water" inline to the fresh water tank and found the malfunctioning valve. The design was also in the water system design documents for the trailer.
It was a $10.00 repair. with no water damage. to the floor. I hope this helps.