Prior to cutting the new geometry the transitions are 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 as you go around the surface of the object, the transition is relatively smooth. It's a cheap but effective trick.

Once 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.

![enter image description here][1]

The dark area just below the blue arrow indicates the flow that your geometry would need to have (seen from the side of that edited face). If you can move the internal vertices to match the curvature you'll get reasonable smoothing.


  [1]: https://i.sstatic.net/fUps3.png