Actually, it's the Indiana SAFE-T system as the State of Indiana has funded all of the transmit sites and manages the issuance of talkgroups and radio IDs. The cities and counties that use the system pay for user radios and dispatch facilities.
Michael, as you've discovered, all of Hendricks County is dispatched by a single dispatch center, the Hendricks County Communications Center in Plainfield. All 9-1-1 calls are routed to Hendricks Communications and all police and fire units in the county are dispatched from there. They use a common dispatch talkgroup for all fire departments. Small fire runs automatically transfer to the 32-HCF-FIRE talkgroup and EMS runs transfer to 32-HCF-EMS. Larger runs will be assigned an OPS talkgroup. Each fire department has different tone-out tones, but that's only useful on initial dispatch. The best you can do is listen for the Avon-Washington Township fire units which will have a unit number with a 14 in it. For example, the engine at the station on US 36 near SR 267 (Station 141) is Engine 141 while the ambulance is Medic 141. The other stations are on Ronald Reagan Pwky north of the Shiloh Crossing shopping area (Station 142) and on CR 525E just south of CR 100S (Station 143).
Avon Fire also sometimes is assigned to mutual aid runs with Wayne Township, Plainfield, Danville, and Brownsburg. Hendricks Communications is somewhat unique in that there's a direct connection between their computer aided dispatch system and the one used by Indianapolis and Marion County. This lets dispatchers on both sides of the county line see what units are available in the other county and assign those units to their runs if needed.