The answer to your original question is that the time depends on he will go not He tells me. He told me he is going/ he will go means that he has not yet left: the commoner he told me he was going means only that he had not yet left when the conversation took place, leaving open the question whether he has gone by now.
The edited question is harder to answer: He told me or He was telling me would refer to a specific conversation. He is telling me or He tells me could be 'historic present'for the same thing, or He tells me could be non-specific, referring to what you gathered from a series of conversations in the past.
(For completeness, he is telling me could also be normal present, but unless you are chatting to a colleague while composing your post, that's unlikely to be useful).
In normal conversation any of them are possible, since the distinctions are too fine to be useful.