[xoxoxoBruce]

Did you see inside the soffits when they replaced them?
The one along the back of the family room is probably warm, moist air leaking out between the upstairs floor joists and condensing inside the cold soffits. Probably the only way to stop that is tear off the soffits and seal between the joists.
The cathedral ceiling "should" have an air space between the underside of the roof and the insulation, soffit vents to draw in cold air plus a ridge vent to exhaust hot air. This air flow keeps things dry, keeps the roof from overheating and keeps the snow from melting and refreezing further down causing ice dams. Ice dams cause the water to back up under the shingles and wet the plywood underneath. Unfortunately this is where unscrupulous builders cut corners.
Where you have an "attic", the same would apply except instead of a ridge vent, you might have vents in the wall at the peak. It would be a good idea to cut an access someplace like a closet ceiling to get a look at how it was put together.