The height, by definition, cannot be negative. That's why it is displayed as a positive in the component properties. The David used a trick with specifying a negative height to effectively invert the component. This have to be done only once, unless you want to invert component back again.
Suppose that there is a dome component with height of 0.8". If you type -0.5 in the component height, the component will become a dish with height of 0.5". if you now decided that it should have a height of 0.4", you should place 0.4 in the shape height box.
Using -0.4 would make it a dome again, with height of 0.4"
In case of rotary projects, when dealing with negative components (created with David's trick or subtracted) it is best to switch off the wrapped view and use flat view instead. The rotary view does not show negative z-values correctly. As the taper initially descends below the zero plane in flat view, it would most likely not look right when in wrapped view. After the shape base height is adjusted, the taper component is effectively lifted and does not go below the zero plane. At this point wrapped view should be correct.
It is important to clarify that the shape height behaviour cannot explain the problems with machining. When changing rotary axis from X to Y, it is important to also remember to adjust relevant machining strategies. In this project roughing involves raster along X axis, which means along rotary axis. After changing orientation of the project in Job Setup form, one should also switch the roughing raster to work along Y axis. The same will apply to finish toolpaths.