I have not been able to find any install instructions for this type of half-round metal dormer that was recently replaced. My guess is the unsealed overlapping seams are not correct, since I can reach my hand inside. The 2nd seam had a single rivet in the middle.
Is the water designed to go into the seams on top and drain out the channels on the sides?
My experience with them is that a sheet metal guy comes out and templates then fabricates. What you have looks like very shoddy workmanship that in my opinion will leak into the structure.