Wiring light sensor OPB704WZ to Arduino Due
You expect that the white surface to reflect the infrared light and the black surface does not.

Your theory is correct; white surfaces should reflect pretty much all light and the black surface should absorb all light. 

The problem is that the black surface is reflecting enough light to turn the photo-transistor on.  

The theory is correct but in the real world this is not perfect. For example a white surface is not completely white. Likewise no black surface is completely black. 

We also know that a mirror is much better at reflecting light than a white surface. The black surface could be shiny. I am looking at my shiny black monitor stand, and even though it is black I can still see the reflection of the window.

I suggest trying with a number of black surfaces (such as paint, card, cloth) and finding the one that works best. I would imagine that chalk board paint would work well at absorbing and diffusing the infrared light. Also experiment with the distance away from the surface. You may have to move it further away from the surface.

If I am imagining your tachometer right, your sensor will see a reflective surface and then it will see empty space (and then repeat). This should work fine. Give it a try.