VAV systems are typically controlled on a supply air set point temperature. If the supply air temperature set point is below the air temperature entering the VAV system, then the cooling coil will operate. Once you run a simulation you can review the rdd file (you must have Output:VariableDictionary,IDF; in your input file to create the rdd file) and choose report variables to view after the simulation completes. Look at the air temperatures (System Node Temperature) and control node set point temperatures (System Node Setpoint Temperature) to see if the controls are the issue. You could simply look at the cooling coil to see what's happening. In your input file a SetpointManager will be used to place a set point at the coil control node, which is typically the coil outlet node. Look at these reports to inspect the operation of the VAV system.

Output:Variable, Cooling Coil Inlet Node Name, System Node Temperature, hourly;
Output:Variable, Cooling Coil Outlet Node Name, System Node Temperature, hourly;
Output:Variable, Cooling Coil Control Node Name, System Node Setpoint Temperature, hourly;