Here is the way it should be at least in my region. The roof edging is installed before the shingling process and is to wrap around the facia and be installed so that the tail end is on the facia which directs the drip or water off and away from the facia when gutters are not being used. Then too, the shingles are to extend over the drip edge or cantilevered over the facia about an inch or two. This also protects the facia when gutters are used or not used. The water is then dirrected over the facia and falls away from the house.
The gutters are to HUG the facia or the drip edge and fit under the cantilever or shelf of the shingles so that the water is diverted over the back edge of the gutter and to fall into the trough. Sounds like your system is taking the water between the gutter and the drip edge.
Does your facia have that 1x2 furring strip around the facia that the drip edge is connected to? If so, then you need to re hang your gutters to attach under the furring strip which will give you the 1 inch cantilever for catching water. you migh be fastened to the furring strip which is causing your problem.
Then make sure the trough is slanted a bit to cause the water to drain toward that down spout.
Come back with more information on how the gutter is attached and if your shingles are cantilevered over the drip edge. If not, you can slip a extender under the shingles if composition to cause the cantilever.