Jacob,
The key here is that in order for one zone to get cooled at night, its fan
must operate. The fan serves ALL of the zones, however, so ALL zones get
air (and cooling and heating)
Most VAV systems require a non-zero minimum airflow to maintain proper
outdoor air ventilation and maintain that scheme / minimum at all times -
even at night.
It's possible to control VAV boxes for zero minimum airflow in unoccupied
periods, but it would be unusual.
In most cases, the fan itself must also have a minimum airflow for stable
operation and to prevent variable speed drive overheating ... but that's
another problem....