What's a word or phrase that could be used to describe a person who needs to see the evidence for a claim in-person before believing it?
If you're looking for an idiom, one that seems to fit is:
This comes from a story in the Christian Bible in which Jesus' disciples are told he has risen from the dead. Most of them believe, but Thomas says that he will not believe it until he could see and feel the wounds of the crucifixion for himself--literally, he says, "until I can stick my fingers into the hole the nails made in his palms, I won't believe it."
He later meets the resurrected Jesus and does believe--but not until he saw it for himself.
Because of the religious origin, this phrase is sometimes used by advocates for blind faith of people who ask them for solid evidence.
I would say of that person that he or she is a show-me one.
He claims to be a show-me person: Demonstrate to me belief without works and I will demonstrate my belief by works.
"I am more of a show-me person. I'd believe in UFO's or aliens if they landed on my head, but that is about as far as I would go." -- David Duchovny.
Consider also incredulous and the expression "be of the school of those who believe what they see, not what they are told," from French "Être comme Saint Thomas, ne croire que ce que l'on voit."
In terms of philosophical positions, pseudoskeptic might work here.