FDTD uses rectilinear building blocks to construct the geometry. Even though you have an ideal disk or sphere, the FDTD will reconstruct them into small rectangles. Thus for circular sectors, it will be discontinuous.
In addition, the import has limited resolution by default. Maybe the key is to increase it. However, different from the built-in geometry, the import may require much more memory. This might be the reason it has limited resolution. I would suggest that you file a feature request: