Adiabatic cooling
Oh my goodness, tried to get my head around that but I seem to be getting too old to learn new things.
I imagined it was just the cold water in the lines sucking heat out of the roof tiles ie the water warms from the heat in the tiles then the heat energy is transferred into the pool leaving less heat energy on the roof.
On a hot day with our cool nights if I am naughty and leave the cover off our pool it will be 23deg in the morning and 30deg in the afternoon.
In 40k litres of water 7deg is a fair whack of energy. Understand much is not straight from the house.
That said if you pumped it around the walls of your house before it went up on your roof it wouldn't cost that much more to pump and give you a more direct benifit as it would be inside your insulated house. Is this an option pool heating companies offer? I don't think it is because as I said I tried googling whether I was imagining the difference the pool heater was making the house and found nothing.