What do you call someone when they don't believe in something then they believe in it when they see it themselves? [duplicate]

Skeptic

Empiricist

Missourian (Missouri is called the "show-me" state)

If you're looking for an idiom, one that seems to fit is:

a doubting Thomas

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.

evidentialist

(philosophy) Of or supporting evidentialism, the doctrine that evidence is of primary importance in questions of belief

Evidentialism is a theory of justification according to which the justification of a belief depends solely on the evidence for it.

Furthermore:

Evidentialism also faces a challenge from the infinite regress argument. In general, responses to this argument can be classified in the following ways:

• Foundationalism: There exist beliefs that are justified, but not because they are based on any other beliefs. These are called properly basic beliefs, and they are the foundation upon which all other justified beliefs ultimately rest.
• Coherentism: Justified beliefs are all evidentially supported by other beliefs, but an infinite set of beliefs is not generated, because the chains of evidential support among beliefs is allowed to move in a circle. On the resulting picture, a person's belief is justified when it fits together with the person's other beliefs in a coherent way in which the person's various beliefs mutually support one another.
• Conditional Theory of Justification (Reliabilism): A belief is justified by a set of beliefs. However, this justification operates conditionally, as it depends on the truth of the justifying beliefs. There is not a need for basic beliefs, but one should note that this type of justification is weaker.
• Skepticism: There cannot be any justified beliefs.
• Infinitism: Aside from these responses, some philosophers have said that evidential chains terminate in beliefs that are not justified. Others have said that, indeed, there can exist infinite chains of reasons.

Of the main responses, coherentism and skepticism are clearly consistent with evidentialism. Coherentism allows evidential support for all of our justified beliefs in the face of the regress argument by allowing for circular chains of evidential support among beliefs. And the skeptic here is utilizing an evidentialist demand to arrive at her skeptical conclusion.

I would say of that person that he or she is a show-me one.

show-me: inclined to doubt or question claims; demanding proof or evidence before being convinced.

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.