First of all, only the dash-two (POWR1220AT8-2) Power Manager devices support HVOUT output voltage of 12V. Secondly, the gate of the hot swap MOSFET does need to be driven to 18V to 20V in order to turn it on. This is accomplished using a few external components to implement a voltage adder. This circuit adds the HVOUT voltage to the 12V rail to provide the bias needed to turn the MOSFET on. The Power Manager modulates this circuit to limit the inrush current which is the basic function of a hot swap controller. The theory of this circuit is described in detail in reference design RD1068 12V Hot Swap Controller with POWR1220AT8 and the circuit is available for evaluation on the Hercules Evaluation board (link below).
Power Manager II Hercules Development Kit