I would say this method of asking a question is a specific way to ask a question by command. For example, if I ask, "When are you going to Japan?" And you speak to me about other things and ignore my question, I will then ask this way "Tell me when you are going to Japan." (Are and you are switched) It's a command basically. Another reason to ask this way is because the person asking is not interested in anything else that person may want to say. I have never asked a question this way because I don't like to omit words and assume the other person knows what I really want to know. I would just ask this way... "Would you just tell me when you are going to Japan?" The word 'Would' made it a question. This is the complete way without omitting any words and the correct form of the question.

The sentence is incorrect. It should be, Tell me when you are going to Japan. It is not a question, it is a command (tell me). Look at this example. Let me know when you arrive. Not, let me know when do you arrive? Your sentence would be correct if Tell me were its own sentence; Tell me. When are you going to Japan? Tell me would refer to something. Another example, I need to know (something). When are you going to Japan? But, I need to know when you are going to Japan.