If you are using a version 2 or newer bridge you can integrate with Siri. You can only put one bridge on one email account. Currently if you setup and connect caseta with one system using homekit then setup an other system using homekit you will have a problem with the first system and homekit.
What happens is that the first system is tied to homekit in two places. iCloud and Smart bridge. When you add the same Apple ID to a second system iCloud keychain will use the newest integration. You cannot change which system Siri connects to back to the first system. Reseting both the smart bridge and the second iCloud Apple ID doesn't solve the problem alone. Both the first systems bridge and the first Apple IDs both have to be reset. Then keychain has to be turned off and turned back on.
If you want to control 2 systems only integrate one with Siri. Sign in and out of the app to switch control from one system to another. It does not matter if you are signed into the app once homekit as been setup as the Apple TV controls the bridge not the app.