It's not as simple as you make it out to be. Granted, wiring a fan to a relay is trivial, and done by science-project schoolkids all over the world, but you can't just grab some bell wire and twist them to a relay terminal and call it done.
You have a motorized fan in your 3rd-floor attic, in a location not normally accessible in day-to-day activities, which is also subject to extreme temperatures. You have a pool control at ground level. If you tried to use a pool automation relay directly, you would need at least 30 feet of wire, one way, and would be subject to voltage drop along the way. You can't just run zipcord to power a fan in this situation. If you wanted to use a second, remote relay, as has been mentioned here, you need to insure that it is enclosed or otherwise rated for use in the attic, and you still need to properly run some type of control wire to the automation controls.
I don't recommend trying to just rig something. Sorry.