It depends on what you are trying to do.

A mesh smooth is typically applied to subdivision surfaces.  The sub division surface could be quad patches, so what you are reading may be the control cage.  If you just want to convert the control cage to triangles, you can use TriangulateInPlace.  The first image looks like it is not triangulated.

If you want to have FBX SDK smooth the control hull and create a triangulated mesh, it is not currently a feature.  FBX does not support mesh smoothing other than storing the parameters in the file.  See kfbxMesh.h for details.

So if you want to obtain the smooth triangulated surface from the original model, you will have to subdivide the control hull yourself (via Catmull-Clark or similar) or have it done in Mudbox before it is exported.

Note that when you subdivide a surface for export, you may get huge FBX files.  I have found these can take huge amounts of time to load and save.