Please start by posting some screenshots that show how you configured an automation with Hubitat to control your lights with your Zooz button controller.
The platform will not send the same event twice for most devices, except for those devices where it makes sense - like Button Controllers.
Can you make sure from your hub's z-wave table that Zooz button controllers are still indicated as button controllers? If they are not, do a power-cycle (shutdown, remove power from the hub, wait 30 secs, then power up. While removing power do it from the outlet end, and not the hub's microUSB connector).
I am asking because I recently had a similar experience out of the blue. Certain Z-wave devices stopped responding to z-wave commands meant for switches. I thought the switches had gone bad, until I noticed they were not marked as switches in the z-wave table. A power-cycle fixed the issue.
I would suggest setting these two options. First one will make it activate even if already activated. Second one will help it decide when it should be "inactive" (a state of the RL not turn the lights off).