The path needs to start and end with segments perpendicular to where you want the ends of the follow-me to be. Standard SketchUp arcs put a vertex at each end and the first segment from that vertex is a chord of the circle, i.e. not perpendicular to the end face. You can either rotate the arc so that it has a midpoint at each face or add little extension segments at each end and then trim off excess after the follow-me.
Follow me starts and ends the extrusion perpendicular to the path so what you are seeing is normal. You can extend the path past the corner a little bit or change the path so it ends perpendicular to the faces at each end.