Is the integration local
And has anyone used it via the HomeKit integration? Does it work well with Siri?
You might want to ask in this thread, but the answer is no. The integration uses Rachio's cloud API.
[RELEASE] Rachio Community (dashboard + hose timers) - 
Custom Apps and Drivers - Hubitat
The Rachio integration for Hubitat is cloud based unfortunately. (Same in Home Assistant too)
I have heard that integrations using Homekit work locally, but unfortunately I have no Apple devices to test that with..
