First of all, it seems that some people are wondering what this thing is;
here are a few pictures, as well as the opportunity to buy one, if you're so inclined.*
Now, I don't personally have experience with this thing, but is it possible that some components inside are axially loaded, and that loading is dependent on the direction of rotation? (For example, helical gearing transmits an axial load to the shaft, and its direction depends on the direction of rotation of the driving gear.) That axial load could conceivably cause the behaviour described (by forcing the cutter into the workpiece in one direction, and upward into a thrust bearing in the other direction).
*I have no relation to the seller!