What happens to manifold pressure reading following a reduction in both throttle and RPM?
I think you misread the question. Assuming you quote it properly,


  To set climb power, you reduce the throttle (manifold pressure)


… so the first step does reduce the manifold pressure and is therefore not subject of the question …


  and then the props (RPM lever). After setting the props you expect the manifold pressure to:


… only the second step is.

In the second step, the manifold pressure slightly increases, which


  On the other hand a reduction in RPM would mean less suction/vacuum so the MP reading would increase.


… you already understand.

So yes, the manifold pressure decreases first—when you retard the throttle—and then increases slightly as you reduce pitch. Just the question only targeted the second part.

The increase won't be back to the original value, because the throttle is still partially closed. With wide open throttle the manifold pressure is (for normally aspirated engine) almost ambient pressure and there is nowhere higher it can go.