The Generic serial adapter (7620) is only compatible with the RS series Aqualink and not the PDA series. You would have to upgrade both pcb's in the power supply then your pda will become a slave device.
Inside your Aqualink power centre you have a main pcb and on the back of that pcb you have a small pcb (cpu). You can purchase an upgrade kit and depending on your pool combination will depend on what upgrade kit you need. So looking at your pool description it will be a pool & spa combination so Upgrade Kit, RS One Touch PS8 and also a One Touch controller needed to program the Aqualink system.