Prior to cutting the new geometry the shading is nice and smooth because the shading is a function of the various face normals adjacent to each vertex. Each vertex uses connected faces to get an average vertex normal. Because each of those adjacent face normals is different around the object, the vertex normals allow for a smooth enough transition around the surface.
One you start cutting into a face, you get new geometry which has a number of vertices which are surrounded by faces which have the same face normals, therefore the shading is 'flat' on those sections.
The way out of that is to carefully adjust the positions of the new vertices such that they follow the inferred curvature, this doesn't have to be exact. as long as you get away from the faces all having the same normals on that spot.
i'll add an image.