My Maya 2018 only matches position of pivot is seems when Match Pivot is used. I use a much clumsier method as I am new to Maya.
1. Match Pivot, now your work object's pivot is where you want it but it is not yet oriented (in my default Maya 2018).
2. Create a Poly Primitive Plane. 10, 10, 2, 2 is good with normal set to X.
3. Match All Transform the plane to to target object (not the work object) Match All Transform does as on tin and the plane has your desired orientation as normal data on its surfaces.
4. Parent the Plane into your work object. This now allows the work object's Custom Pivot actions to be applicable to it's child objects. We can Orient.
5. Select your work object and enter any transform mode. Then turn on Custom Pivot mode [D].
6. While in custom pivot mode, hold down [CTRL] and hover mouse over a surface of the child Plane, notice the cursor indicate Orient. Left click.
7. Bake pivot if you're feeling risk averse.
Note: on some occasions, it may be necessary to rotate the Plane to correct desired up-vector. Rotate in Tool Snapping mode [J] in 90°. Orient again.