No, you're not wrong. I think that's a good question.
There are two schools of thought on emotions and interpretation. There is the more traditional European school according to which interpreters should speak in a monotone. Emotions don't enter into it. I believe that today, many clients prefer a more emotional form of interpretation that reflects the emotions behind the words. I used to teach at the University of Ottawa. My view is that interpreting what people say amounts to more than just words, but also the ideas underlying the words, including emotions and other aspects.
So I think it's all right for an interpreter to capture some of the emotion that underlies what you, the members, are saying. But the interpreter is not feeling your emotions, just representing them.