On pump unloaders have multiple designs but they all do the same thing, that is they allow the pump to get a running start before it has to work and compress air. On larger pumps with heavy fly and large diameter pistons, that is alot of inertia for the motor to overcome from a dead stop, adding in the force on the pistons from compressing air during this cycle can be just to much for a given motor size. The unloaders allow the pump to reach running RMP before compression of air into the tank happens. On the Saylor Beall, IIRC they use a centrifugal unloader, where the pump has to meet a specific minimum RPM before it will start compressing air and directing it into the tank. Other makers use different methods for unloaders. Quincy for instance uses a hydraulic method that sens oil pressure in the crank case.
They are plumbed into the tank to sense tank pressure, sometimes directly, sometimes through a control valve circuit. Sorry, but I'm not familiar with Saylor Beall pumps to know for sure what all yours needs to go through.
The after pump unloader, does the same thing, but instead takes residual pressure off the exit valve and plumbing between the pump and usually in tank check valve. Again different makers use different methods to accomplish the same tasks.