An acceptable version of OP's pic.

Shingles aren't left hanging in the air

If your builder can not tell you what is wrong with that, you selected the wrong builder.

The fact that I can see the raw plywood is a HUGE red flag. The aesthetics are bad but the actual construction is worse.

If it were me, I think I would have notched the barge board (or rake fascia) and extended the gutter 1/8th inch past its outer face, and put a metal (copper) on the top of the barge board that extends past the gutter. I would do a sketch but I am off to a late dinner.

Another part of the solution may be to add another downspout. It appears that part of the problem may be a long gutter run, causing the end furthest from the existing downspout, to get proper drainage, is too high.

^^ Yes, it appears that the top of the gutter is actually above the plywood roof deck. Agree with everything Mark said in his last two posts. It appears that the gutter installers are idjits.

Where I live a gutter is placed so that ice sliding off of it would not hit the gutter. That also allows the end of the gutter to be hiden behind the rake trim.

I suspect there was insufficient facia trim for the gutter to be installed lower.