Export with Split-Per-Vertex-Normal checked true. You will lose smoothing groups, but no tessellation issue and no UV issues.
Eric Ketchum
Not only did that not fix the UV issue, but it also caused erroneous tessellation on the side of the mesh, which caused infinitely thin extruding sections, with the peaks seen on the other mesh:
Make sure that your normals on the top and bottom outer edges are NOT set to perfect 0,0,1 values, ie leave them with the original 3 normal averages at the corners or 2 normals along edge.
Ultimately though if you Can please upload the fbx of your mesh?
Eric Ketchum
I believe the fact that the normals are averaged is causing the UV issue, but here is my FBX: https://dl.dropboxusercontent.com/u/30847069/TessellatingCube_Error.fbx
Hey Hoeloe -
I have entered a request for our engineers to look further into this tessellation issue. I will keep you informed as we continue to invesitgate, for reference it is UE-4923.
Thank You
Eric Ketchum