depending on the tubing, some is exceedinglly soft and can pinch easily.
some is just short of steel tubiing and will not pinch off.
I have used a stepper with a roller, much like a peristaltic pump, but just one roller that is off center. used it to drip feed lubricant on a cutting tool.
if your requirement is that no two can EVER work at the same time, you can have one drum with cams and each tubing goes under one cam. only one cam would allow flow. you could make with wood drum very easily and with a cover, it would look good.