It will vary depending on if the synthesizer is a full analog synth, or a hybrid synth with digital components. The way that analog synthesizers with digital components (one of the first of which was the Prophet 600) typically work is that there is a separate control A/D and D/A, which actually sits in between the potentiometers and the synthesizer engine. In older synthesizers (such as the Prophet 600 Prophet 600 schematics), there was only a single A/D and D/A pair, which are multiplexed by using several sample and hold circuits. In any case, when you store a patch, the voltages of the controls are digitalized using the A/D and stored by the microcontroller into whatever non-volatile memory. When you recall a patch, the D/A generates the control voltage and bypasses the potentiometer.
Of course you are correct a sudden "override" of the physical controls by either recalling the patch or external MIDI control can be jarring and quite 'unmusical'. Therefore, different synthesizer manufacturers have adopted different methods to overcome this problem. I know that one manufacturer uses a weighted interpolation, so that if you recall a patch and then start "twisting the knobs", cleverly designed circuitry will allow the knob to operate from the starting point that was stored in the patch, but also assuring that you cannot exceed the normal bounds of the control.
Another problem which can happen is because the controls are sampled, sudden or precise movements of the control potentiometers can cause stepping or other artifacts in the sound. The was very much a problem on the Prophet 600 and other vintage analog synthesizers with patch memory, but is less of a problem now that processors and A/D and D/A technology works at higher speeds.
Finally, now that I've had a chance to look at it, it seems that the OB-4 voice programmer works the same way: according to this schematic. Of course, this is only a voice programmer, and not a full MIDI controlled synthesizer like the Prophet 600, so only the second problem is an issue. It is not meant to be used to modify the parameters of a sound in a real-time performance.