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If you tessellate some surface, it is no longer easily possible to calculate the real hit point based on the hit point of the tessellated version. Thus what you have to do is either:

1) Implement an analytic intersection routine with your curved geometry and add this shape as an Embree user geometry.

2) or, increase the tessellation rate to better approximate the real hit point.

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What you are asking for are PN-Triangles (http://alex.vlachos.com/graphics/CurvedPNTriangles.pdf). However, they still have discontinuities of the geometric normal along the edge.

Embree supports Catmull Clark Subdivision surfaces, which is a smooth surface representation. Maybe that is an option for you. However, internally we implement this primitive also through tessellation, however, we cache that tessellation to bound memory consumption.

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