Greetings, and welcome to Apple Support Communities Zedox!
From your post you’ve mentioned that Siri is working with your iPhone but no with your headset.
Check this out: If "Hey Siri" isn't working on your iPhone or iPad It goes over the what to check for if “Hey Siri” isn’t working.
Next, understand how Siri works with more than 1 device: How 'Hey Siri' works with multiple devices - Apple Support Specifically check out “What to do if the wrong device responds to ”Hey Siri””
If you’re not using an Apple headset, check out their developers site. You'd want to see if they have instructions how to use the microphone, or what is needed to connect to Siri on their device.
We hope this helps!