How do I prevent Siri from listening and interrupting conversations on iPhone?

Instead of using "Siri" as the Activation word, change it to "Hey Siri". This will weed out false activations, for example if you say "surely" it may activate, where if you had "Hey Siri" as the activation word it would not.. Of course, it has to listen for this activation word and something was said that sounded like the activation word for it to respond. You can turn Siri off and then turn it back on to set it up again to further assist in false activations.

If you don't want Siri listening at all for the activation word, then you can shut it off completely and manually activate Siri on your device whenever you want. That way you would never have to worry about false activations.

Siri is only invoked with “Siri” or “Hey, Siri.” Evidently you are making sounds that Siri believes invoke the assistant. There is no privacy issue.