Hello bwa2011,
Welcome to Apple Support Communities!
We want to help make sure HomeKit is recognizing when you are home like you'd expected.
To help us isolate the issue, does this happen with all automations or only certain ones? If you create a new one while using iOS 16, does the same thing happen?
Please also check for any pending iOS updates to iOS 16.1.1, which can help make sure the software is working as expected. This Apple Support page can help get those updates installed: Update your iPhone, iPad, or iPod touch - Apple Support
"Update your iPhone or iPad wirelessly
- Back up your device using iCloud or your computer.
- Plug your device into power and connect to the internet with Wi-Fi.
- Go to Settings > General, then tap Software Update.
- If you see more than one software update option available, choose the one that you want to install.
- Tap Install Now. If you see Download and Install instead, tap it to download the update, enter your passcode, then tap Install Now. If you don't know your passcode, learn what to do."
We hope this helps to resolve the issue so the automations start as soon as you arrive home like you expect.
Cheers!