It sounds like you are using a double solenoid valve to control the Venturi. Generally, double solenoids are used on pneumatic cylinders when you would like the cylinder to push and pull with great force. This is done by controlling the flow of air through two controllable valves; hence double solenoid.
You only need a single solenoid valve such as the Festo or single solenoid SMC. When you want your suction cup to work the solenoid valve must be open allowing compressed air into the Venturi pump and causing the suction cup to, well suck. When you don't want suction the solenoid valve should be closed, the suction will be relieved by flowing back through the Venturi and your cup will stop sucking.
FYI, FIRST has a
pneumatics manual on their website.