Looking at the stock regulator (not used with this unit) you have black, white, and green wires connected using spade lugs. These are ignition power (black), field coil (white) and ground (green).
The Electrex unit connects through the big plug to the alternator 3 phases (all yellow), ground (green), and battery "+" (red).
So there's already a ground connection to yoyr new reg/rect. It needs the other two to work - black and white.
So these wires are separate. Remove the black and white wires from the old regulator. They will plug right into the Electrex wire spade terminals. You might need a bit of electrical tape to insulate them, the wiring harness terminals have plastic vovers but these might not be completely covering the metal bits.
The regulator needs switched ignition power to run the field coil. If it only had battery power, it would drain your battery rapidly trying to make power when the ignition is off and the motor not running.