By Design: Normals (and positions) are always affected by blend shapes/morph targets regardless of the recompute tangent mode. 4.13 is wrong.
In 4.13 if you imported a skeletal mesh with a blendshape and run the blend shape. The normals are not recalculated.
To Recalculate the normals during runtime you need to edit the Console Variables.ini and add
And then on the skeletal mesh you have to enable Recompute Tangent.
In 4.14 release.
Without enabling anything, Skin cache or the recompute tangent (Skin cache needs to be on for this to work) tangents are recomputed on blendshapes anyway.
There's no existing public thread on this issue, so head over to Questions & Answers just mention UE-38360 in the post.