The 12V system is supplied by a solid state DC-DC converter from the high voltage system whenever the car is "Ready" (whether you're moving or not, and whether the ICE is running on or not) or when the car is actively charging (not just plugged in).
The view from the 12V side is similar to a traditional car -- the DC-DC converter supplies a constant ~14V just like an alternator does, and the battery itself is only actually supplying power when the car is off, including of course to bring up enough control to start it (and since our cars don't need a 12V starter motor to do that, the actual power required to do that is much less)
Beware -- I used "Ready" above to mean starting the car normally (pressing the Power button WITH your foot on the brake) as opposed to "On" (press the Power button twice WITHOUT your foot on the brake), which works like an old key-start car when you move the key 2 positions but don't hold it farther to start. In "On" mode, like accessory mode, you can't drive and the HV system is, ironically, off, and you are draining the 12V battery to run the radio/fan/etc.
Edit: Landshark said similar, much more succinctly, while I was typing this
