Capillary action occurs when the molecules of a liquid feel a greater attraction to the surface of a solid than to each other as they travel along that surface. Therefore, when water passes over the edge of the roof, it will remain attracted to the surface of the drip edge and will run behind the gutter. You might see water dripping from behind the gutter or even running down the wall during rain. If it lasts long enough, water stains will start to form on the wall.
If you notice this happening to your house, but the gutters seem to be glued to the wall, the problem may be the leaking edge. The problem is, in part, that the drip edge does not leak. It may have been too tight when it was installed, causing it to be too flat. It's not really a sewer problem.
The fact that rainwater ran through the fascia was a problem that needed a solution anyway.