Audi alteram partem (or audiatur et altera pars)

Audi alteram partem (or audiatur et altera pars) is a Latin phrase that means, literally, hear the other side. It is most often used to refer to the principle that no person should be judged without a fair hearing in which each party is given the opportunity to respond to the evidence against him.

As a logical error, it refers to the fact that people will argue from assumptions which they don't bother to state. The principle of Audiatur et Altera Pars is that all of the premises of an argument should be stated explicitly. It's not a fallacy to fail to state all of your assumptions; however, it's often viewed with suspicion.

The premises of an argument are often introduced with words such as "Assume...", "Since..." and "Because...." It's a good idea to get your opponent to agree with the premises of your argument before proceeding any further.

The word "obviously" should not be used, though. It occasionally gets used to persuade people to accept false statements, rather than admit that they don't understand why something is 'obvious'. So don't be afraid to question statements which people tell you are 'obvious' -- when you've heard the explanation you can always say something like "You're right, now that I think about it that way, it is obvious."

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Principle that states that all premises of an argument should be stated explicitly, arguing from assumptions not stated This is not always a strict fallacy per se, but illustrates a principle that is often broken during discussion and should be avoided when possible.

X: "I believe in God".
A: "There is no evidence of God's existence".

"A is guilty of "jumping to conclusions" in regards to what he considers evidence, for the criteria for evidence is an assumption and was not explained"

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Well... it is a generally accepted fact that there is no evidence of God's existence, that you cannot prove God exists nor that God doesn't exist. Accusing "A" of "jumping to conclusions" is like accusing X of "jumping to conclusions" because he doesn't state properly what he means with "God" or "believe".

No...

This is more like some people discussing about an issue, and then someone gets into the discussion, and after a while one of the people in the discussion tells the newcomer that he should be quiet, because he doesn't know what they are talking about, referring to another discussion, that was not in any way or manner mentioned in this discussion earlier.