I've got the same problem but, the cause is a little different.
For me, the shingle does not overhang far enough to reach the gutter and where ever there is a gutter nail, it drips onto the nail and runs behind the gutter.
Your problem sounds like it could be the cause of shingles going bad and/or ice damming. If the water does not roll off the shingles but, backs up into the shingles and gets behind the drip edge then the water will exit between the fascia and the gutter. At a minimum, you'll need to replace the curled up shingles.