If someone came up to me claiming to be a time traveler, I would just say "Alright, prove it". If they're from the future, they could show me a piece of their ID or a future news article. If they're from the past, they could show me a historical photograph of them in it. Afterwards, I would ask them a bunch of questions such as "where are you from?", and "can I have a copy of your time machine".
See? Asking questions is perfectly normal. People who shut down questioning have something to hide.