Even already quantized control voltages should not be used as CV source for the module. In this case similar problems may occur if the voltage steps of the incoming signal are close to the voltage thresholds of the A-156.
I can't see how this is relevant in this context. If the module is correctly calibrated a voltage that isn't close to the thresholds should always be correctly quantized. It doesn't matter if it comes from another quantizer, a keyboard or a random S&H.
I don't have any experience with this VCO, but I see that it supports different scales. Do you have the same problem with all scales? Have you tried to give it controlled voltages around the level that should result in a C to see if you can get that C at all on how much it's off?
The calibration mode seems to be quite helpful. As I understand it, it will report the measured voltage. What's it saying about the C that's played as a C#?