The Follow Me tool requires that the first segment of the path is perpendicular to the profile and the end face of the extrusion will be perpendicular to the last segment in the path. When you use the Arc tool to draw an arc, the end segments aren’t perpendicular to the radius of the arc. You can see that more clearly when you use fewer sides for the arc.

The easy solution is to use a circle and rotate it so that edges are parallel to the axes. Then divide the edges at the midpoints so the first and last segments will be perpendicular to the profile.

Here I’ve drawn a circle, rotated it so that sides are parallel to axes as shown.

After that Follow Me does what you want it to do.

Note that if you set up the profile so it is not perpendicular to the first path segment SketchUp doesn’t rotate the profile. It projects it to perpendicular. Usually it’s not that critical but it does result in the shape being changed.