If you want your normal maps computed in Maya to render without such distortions in Designer, you need to :
* make sure that the tangent frames (TBN) are saved when you export your mesh (which implies that you use a .fbx file to export the mesh, as .obj files can't contain tangents)
* in Designer, un-tick the checkbox "Always recompute tangent frames". This is the default setting but you may have changed it by accident. It is in Tools->Preferences...->Editors->Mesh
As Wes said, the problem comes from the fact that all programs need the tangent frames to "decode" the normal-maps, and there is no standard way to compute them. Maya uses one, Max another, Unity yet another, etc.
At the moment, Designer can either use the tangents provided in the mesh (if any) or recompute them (if none, or if the aforementioned checkbox is ticked). When recomputing the tangents, we use the same algorithm as in Unity. We plan to add options for using other algorithms in the future.