Blendshapes are applied as deltas to the vertices according the set weight. Blendshapes primarily affect the vertex position, but if normals and tangents are set to 'import' they will also be modified. The model attached to this case is set to 'import' normals for blendshapes. These normals are authored in the DCC tool and are read from the FBX file.

The RightForeArm_02 blendshape is quite extreme (you can observe this by setting the weights of all other blendshapes to 0%, and just this one to 100%). I presume the normals for the blendshape have been calculated based on this pose. In the animation the extreme vertex position is compensated by RightForeArm_01. Thus providing a more normal shape. But the normals that are blended in are not necessarily corrected by the other shape. Thus resulting in the observed artifacts. A solution would be to author the normals for the blendshapes in the DCC to be correct for this setup.

Looking at the use case here I think you can get away by only applying corrective blendshapes to the vertex position (setting the blendshape normal option to 'none'). Alternatively, you can recalculate the normals at runtime with some scripting. However, do note that this is rather costly, as it requires baking the mesh and recalculating the normals afterwards. We do not support normal recalculation as part of the deformation process.

Note: please be aware of the following issue. When the Model Importer is set to 'Import' normals for blendshapes, but there are no normals present (for blendshapes) they will be automatically calculated for you. Unfortuntaly we cannot detect this and thus are not able to provide a warning message. Having the normals calculated for you can result in undesired effects too:
https://issuetracker.unity3d.com/issues/artifacts-are-produced-when-using-multiple-imported-blend-shape-normals