Cz process operates with two opposite rotations (melt and seed's rotations). How these rotations prevent growing imposed by other facets' directions (Other than that perpendicular to the axis of rotation-of seed?
Any connection between the (ingot, crucible) rotation rates and crystal growth direction is a bit indirect. The first question to ask is why there is rotation at all. As it turns out, the rotation(s) perform two very important tasks, one of which is what your question is about.
The major problem to be resolved in crystal growth is maintaining a constant temperature across the face of the crystal. The enthalpy of crystallization has to be removed from all across the interface, and this is a mixed thermal diffusion and fluid flow problem. The rotation speeds of the ingot and crystal are adjusted to enhance the fluid mixing and even out the thermal profile. Keeping the interface generally flat means that the ingot grows in the appropriate direction (which is what you asked about).
The second major task is closely related, and that is maintaining an even distribution of impurities (mainly the dopants, but C and O also) across the diameter of the wafer. This is one reason that all large (150mm and larger) silicon wafers are doped with boron - it distributes better and results in more uniform doping across a wafer, quite important for modern CMOS technology. The uniform incorporation of C is critical as well, since it is required for mechanical strength (float zone silicon, low in carbon, cannot support itself in a hot furnace anneal at current wafer diameters).
An interesting read is Fumio Shimura's book 'Semiconductor Silicon Crystal Technology' (Academic Press, 1989).