Hello,
So, HomeKit is a framework that allows secure integration of accessories and Apple devices. It is there for security reasons and ease of use. Some random person turning your lights on and off isn't that big of a deal but if you had a camera accessory that's where the value of the HomeKit framework really increases.
The issue you are running into is that your accessory is trying to integrate into Siri through that framework. For their integration to work you would need to have added the accessory into the Home App. You don't have to use the Home App but their app needs to use your Home App for it to fully integrate. Once you add the lights to your Home App you can use them with Siri and continue to use the app from the local company without ever opening the Home App again.
Another option would be to create a custom shortcut using the Shortcuts App. This is less likely to be available because the app that came with the lights would need to have been made with actions available to use with the Shortcuts App. You can use Siri to run Shortcuts and when you create a shortcut called "Turn all lights on" that will take precedence over the standard system command that uses the HomeKit framework.
Use Siri to run shortcuts with your voice - Apple Support
"Note: If the shortcut’s name is the same as a standard Siri command (“What time is it?” for example), Siri runs the shortcut instead of the standard command."
If the app was made with this available you would see it in the "App Shortcuts". are of your Shortcuts App. Here you you find "Turn on (App Name) Shortcuts with Siri" and a shortcut that the app created which ties directly into their app rather than using the HomeKit framework. If the command you want to use is not listed you could use the premade shortcut to create a new one which you pick the name of.
Run app shortcuts on iPhone or iPad - Apple Support
"Run app shortcuts on iPhone or iPad
Many Apple and third-party apps include built-in shortcuts that automate app features. If an app on your iPhone or iPad has available shortcuts, they’re shown in the Shortcuts screen (iOS) or Shortcuts sidebar (iPadOS), in the App Shortcuts category. You can run these shortcuts from the Shortcuts app, and you can also include these app shortcuts as an action in your own custom shortcuts."
I hope this helps.
