I know that I am supposed to ask follow-up questions in my technical interview, but do I need to justify my question?

You can follow-up your question with 1 or 2 short sentences, but you do not want to go into too much exposition, as this might leave your interviewer confused. If you asked about the user’s age, then you might explain, “If the product is being used by young children as opposed to teenagers, we need to make sure that we are thinking about additional safety features.”