If your drippers are always higher than the reservoir level and the water is pumped, as in your drawing, the drippers will provide the same function as air will enter there and water will flow back to the reservoir when the pump shuts off.
If the containers are ever lower than the reservoir level you will need to provide a means of stopping water flow because just shutting the pump off will not work. The water in the containers will try to meet the level in the reservoir and the flow is maintianed by gravity.
In your diagram, if it were me, I'd provide a drain line from the containers to the reservoir. The system you are showing might work but you are asking for a flood sooner or later.