the roof edge or drip line or intersection of the edge with the gutter is quite important.
A perfect union of guttering and asphalt comp shingles should be that first, the gutter is installed at a slight fall that will naturally divert water from the roof to that areas down spout. Then the water racing down the slope of the roof should fall directly into the gutter trough and be carried off.
The gutter should be placed on the facia so that it is below, as David said a touch to that the running water will fall correctly. The composition shingle ends should cantilever a touch or about 1/2 inch over into the gutter trough so that it falls into the gutter. Due to capillary action, some water will fall over the cantilever and creep under the ledge and drop down between the gutter and facia. This is where the placement of the gutter is crucial to be below the ledge and hanging over the trough.
The quickest way to cause facia rot and damage is when the trough of the gutter is too far from the comp shingle drip edge and the water goes onto the facia and misses the gutter.
you should inspect each foot of the gutter and install new fasteners that will ensure this occurs all around your home.
The fasteners I like are relatively new. They are attached with a long 3 inch screw and clamp onto the front and back of the gutter and when the screw is driven it actually snugs the trough up to the facia and there for under the ledge.
Now, where some novice roofers forget to do is to make that first course of roofing starter row not cantilevered enough over the facia or drip edge. When this occurs its very hard for a gutter to work as designed.
This can be corrected by lifting up the first course of shingles and installing a new row that will cantilever over the trough more.
With some spare time and a ladder you can make this work right for you.