Let's analyze the part tell me that you miss me back
tell is a transitive verb here and like transitive verbs are wont to take objects, it takes me as its direct object. So far so good.
What about that you miss me back? What role does it play?
You tell someone something, right? (A lie, truth, etc.)
That something must be a Noun Clause or a Noun Phrase. Thus, that you miss me back has to be a Noun Clause here because it functions as a mini-sentence within a bigger sentence (that is, it has its own Subject and Predicate and carries meaning).
What about the syntax of the Noun Clause itself? Let's see:
As pointed out earlier, it has its own Subject and Predicate— you and miss me back, respectively.
Finally, concentrate on the bit miss me back . Again, the transitive verb- direct object- modifier combo. Clearly, back here modifies the verb miss as it tells us something about the way in which the singer wants to be loved: he wants his love to be reciprocated. Thus, it serves as an adverb.