PG9HRDW8 bell wiring issue

In general, yes if there is a separate power supply for the sirens, that should be used with a relay. The Hardwire PowerG manual on page 16 discusses using the PGM terminals to trigger devices. The PGM can be used to trigger an appropriate relay, which then switches the power coming from your power supply.

To best assist with options, we would need the model number of the sirens so we know the power requirements.