What I meant by "controlled by software command" was that I intend to send I2C commands to the UCD90120A to command it to turn on the power supply.
I now have an eval board and, by trial and error, determined the undocumented behavior I need.
I have assigned the control of the power supply to one of the rails. Turning on this rail turns on all of the power supply rails.
Turning on the other rails enables voltage monitoring of those rails. Turning off the other rails turns off the voltage monitoring of those rails.
I will experiment with sequencing such that turning on the 1st rail causes the other rails to turn on, but I worry that the off sequence may get hung since turning off the other rails will wait forever since they don't actually turn off until the 1st rail shuts off.