After years of dealing with ice dams, I put a new roof on three years ago, with 6 feet of ice and water shield wrapped over the joint where the roof meets the fascia. In each of the past two winters, I still get the ice dams. I know I have poor insulation in the attic. However, water appears to be getting into the soffit – I get icicles from the soffit vents and it runs down the side of my house. My roofer claims he has no idea what’s happening and blames condensation.
I don’t think you have ice dams, unless they are just above the shield designed to protect the roof under the shield. I think your problem is the gutters, which sound as if they are overflowing. All gutters overflow when they ice up, but yours continue to overflow when all ice and snow is gone. That is because water is dripping or flowing near the back of the gutter, not down the middle, where it should. If it flowed too close to the front of the gutter, it will overflow the front of the gutter, with the resulting flow from the soffit vents and down the sides of the house. Have a gutter man over to make adjustments. More insulation on the attic floor and a ridge vent will prevent ice dams best.