First, you can say "tenga un buen día (don't forget the accent)", but not "tengas un buen día". In this case you should say either "ten un buen día" (if you use "tú", in Spain for instance) or "tené un buen día" (if you use "vos", in Argentina for instance).
But this is in theory, because at least here in Argentina we say "que tenga un buen día" or "que tengas un buen día". Here one employs "tengas" because it is the subjunctive, not the imperative, as in the previous case.
Secondly, the answer to your question: "tú (or vos) también", and "usted también". So you were right.
Cheers,
Sextus