The sketch is of a high reservoir, with multiple level-controlled smaller tanks.
So, it implies that the (lower level) tanks are equipped with a valve that
shuts off the water when a target level is reached: it's just like the
shutoff mechanism in the tank of a toilet. There's a float, which operates
the valve. It doesnt equalize gallons per day, though, just level-in-a-tank.
So, you can definitely find items at a hardware store to build such a system.
If, on the other hand, you want to partition a water source to multiple
destinations based on delivered water volume being equal, the usual
approach is to use a timed valve to a pressurized manifold, and use
matched emitters (i.e. drip irrigation controlled-flow drip fittings).
The physical principle of these emitters is the Bernoulli effect, they
are fabricated so that too-fast water flow in the valve pulls the
aperture shut (this sounds hard, but it isn't). Over a range
of water pressure, the drip rate stays nearly constant. They usually
require pump pressure (or water-utility pressure) though, would clog
if you just used a few feet of gravity-driven flow.