Correct, just directly attached and left on, wide open. The toilet valve manages the pressure, fills the tank as necessary (just like your toilet) and turns off when the tank is full. The water nipples are just gravity fed from the tank. No need for any timer as the toilet valve fills when...
The toilet valve manages the pressure. I leave mine wide open from the spigot and have tested it (and just flushed the system) using a drain valve on the end of the system. No issues at all.
Thank you VERY much for the detailed post. Here are a couple of pictures of my system, obviously adapted to fit my chicken tractor. In the exterior picture, the water tank is on the right and I'm able to keep about 2 weeks or so of food in the one on the left (PVC was sold in 2' pieces so I used...