You are correct that OpenStudio does not currently allow you to assign the zone's DesignSpecification:OutdoorAir object to the AirTerminal:SingleDuct:VAVReheat or AirTerminal:SingleDuct:VAVNoReheat terminals. Therefore, when simulations are run, the airflow for a given VAV terminal is governed by the load and bounded by the settings in the VAV terminal object itself. As you noted in the documentation, it will not control for minimum OA flow.
Traditionally, VAV systems have operated in this fashion (VAV terminals not knowing about OA). In order to ensure that each zone is properly ventilated at minimum flow, designers use the multi-zone ventilation rate procedure calculations from ASHRAE Standard 62.1 to determine the overall OA flow rate for the system. These calculations often result in a full-flow OA flow rate that is significantly higher than what you would get by simply summing the OA from all zones. You can enable this calculation method in OpenStudio by clicking on the AirLoop and changing the System Outdoor Air Method from ZoneSum to VentilationRateProcedure. Note that this calculation is sensitive to the minimum damper positions in the terminal. If you have a VAV system, you should use this method. When you do so, if you see that your system is now running at 100% OA, try to determine your critical zone and increase the minimum damper position in that zone. My rule of thumb is to start with a minimum position of 30% for zones with an OA requirement less than 0.2 cfm/ft2, and a minimum position of 70% for zones with higher OA requirements, then fine-tune damper positions as needed.
The ability for a each VAV terminal to monitor OA and adjust in real-time is called "Multiple-zone VAV System Ventilation Optimization Control," and this was not required until 90.1-2010. In order for systems to be able to do this type of control, they must have DDC control of terminals. The ability to assign a DesignSpecification:OutdoorAir to a terminal and have the terminal adjust accordingly was added to EnergyPlus enable this type of control. We are going to enable this feature in OpenStudio soon. However, depending on your particular scenario, your system may or may not actually have this type of control.
This ASHRAE article by Dennis Stanke of Trane gives a good overview of the multi-zone calculations for design conditions.
This other ASHRAE article by Dennis Stanke of Trane gives a very good walkthrough of the 62.1 multizone calculations during operation (aka Multiple-zone VAV System Ventilation Optimization Control) if you want to dig into this deeper.
