Usually, automatic rejection means rejection by certain predefined process/criteria with no exception. (ie. tells you why) Depends on the context, "you are automatically rejected" can also mean that you are being rejected by certain criteria/algorithm, not decided by a person. (ie. tells you by whom). Of course, it can also refer to the predefined process/criteria (ie. why) Sorry if I have made you more confused.

It means "we have rejected you right away" as in something is already stopping approval. Is this an online application? If so, it may mean that the computer system already saw something to reject the whole application without a human being looking it over. "Auto" often means computer or machine done, and "automatic" means "instantly." Hope that makes sense :-)