I would not use Spin Tool for this particular purpose, closed surface of revolution. Remove doubles, a necessary step, did not solve the problem. My problem was a hidden internal face problem. Hidden faces are bad.
My initial actions produced an internal face with Spin Tool. The face of the initial mesh.
I had to remove edges and one internal face and then bridge edge loops to get the mesh in good form. The extra work seems unnecessary. Consider sleuthing down an internal unwanted face.
Perhaps the best evidence is that loop cut seems to have difficultly with the resulting mesh. What appears visually as a loop has failed with Loop Cut. It has simply created difficulties in your situation.
Finally I [deleted face only] before the spin tool and got the correct results. If felt if I were smacked in the face with a whipped cream pie.
I would use Spin Tool for corners of edited cylinders.
Consider Screw Modifier firstly. (Array Modifier if you feel adventurous)
I applied the Screw Modifier. Loop Cut worked as expected.
Followed by Smooth Modifier.
You might also just use proportional edit to achieve your [spin/lathe] shape.