Useless Gutters

We have a new home with a metal roof and when we moved in we had gutters installed. While I know the gutters catch a lot of rainwater because we have two rain barrels that are fed by the drain spouts, we also have a lot of spots along the roof where the gutters leak (?). I'm not sure the correct term but when I climb up to look at the gutters I can see where they bow out a little from the edge of the roof between the spots where the screws are placed and the water is falling between the roof and the gutter. I contacted the gutter contractor and they told me the roof should have an overhang of 2.5 inches and the gutters will work fine. The roof has an overhang of 1.5 inches. I asked the contractor if 2.5 inches is in a building code or somewhere so I can ask builder why we don't have more overhang, however, of course now I can't get contractor to respond. I can't seem to find a consensus online for the correct overhang. Can anyone help me? I'm just trying to figure out if my roof is wrong or my gutters are wrong so I can fix them!! I have a video of my gutters during the rain if it would help explain what happens as I'm sure I'm doing a poor job of articulating it.