You are correct. It may not be that easy. Most zwave relays allow an input so you can wire in a switch to control them. The switch could be a regular light switch but the it would not switch power, it would just let the relay sense (with low voltage) if it is on or off. Usually the zwave relay treats the input like a three way light switch. (If the state of the switch changes then change the state of the relay). That way you have full control from both the switch and the through zwave and ST.
If the Hayward is outputing 110v then you would need to put a normal relay on its output. When the power comes on then contacts in the relay close. Those contacts would be connected to the input on the zwave relay. Zwave relay would have to always have power so it can stay connected.
Relay something like this:
https://www.alliedelec.com/product/american-zettler-inc-/az2280-1c-120af/70132401/?gclid=CjwKCAjwg-DpBRBbEiwAEV1_-MloyIk1ru02I55Ze3wXEqeJsNOlPPfnUZ7GJGf4DqPU0pD6wDU4-RoCbYUQAvD_BwE&gclsrc=aw.ds
or
One problem may be the three way nature of the zwave relay input. If you switch the state of the relay from ST then when the Hayward went on the relay would go off. However, if you don’t normally change it from ST it is simple mater to fix it if it got out sync.
A little research and on the association is due. If you have questions ask. Zwave Tweaker is a custom device type intended for temporary use with zwave devices. It can be used to configure associations between devices.