rdnelson,
That is correct. The pump will run off of an outlet controlled by Apex. Thus, the switch and the outlet are related ONLY through programming. Essentially, the programming for the outlet is as follows (pseudocode):
If Pushbutton_Switch = OPEN Then ON (if the state of the pushbutton is ON, then turn on the power to this outlet)
It's no different than how the ATO pump connected to Apex is programmed. If the float switch = OPEN then the outlet which powers the ATO Pump would turn on. This would also be similar to how alarm systems work. If the door sensors are far apart, the state changes (OPEN or CLOSED). The control panel which the sensor is hooked up to senses the change in the state and activates the buzzer, sends a signal to the monitoring station, sends emails, etc....
So, putting aside everything else, do the float switches and/or door sensors work based on some current flowing through them? In other words, does the break out box send a continuous current to float switch and detects when there is a break in that loop? Or is the current already inherent within the float switch or door alarm sensor based on the magnetic properties it's design is based on?