Is a solenoid piston strong enough to lock a water tubling?
The pump you are looking at is to powerful for you application: 350 liters/hour, or little less than 5 ltr/min. It will fill a 250 ml glass in about 3 seconds! 

The solenoid cost you $5 a piece, but you still need a valve and a way to attach solenoid, valve and tubing.

Also, your idea means liquids will get mixed inside the tubes. And nobody wants a trace of whiskey in his Vodka Screwdriver.

You must visit The Inebriator, a cocktail mixing machine. His design have one tube for every bottle pouring liquid into the glass.



As they note, they have in version 2.0


  Switching mixers from a pressurised system with valves to using pumps
  – This slows the pouring, but vastly simplifies the machine as a
  whole. We have a capacity for 16 pumps


They don't use valves, but pumps. I recomend a peristaltic pump ($7 on Aliexpress), like this:



They don't touch the fluid, easy to mount, and are a very precise delivery mechanism, like in this video https://youtu.be/GdTUIwj5ros, showing an Arduino controlling a pump to 1ml precision: