Hola Zach,
"Hablas" is the second conjugation for TÚ in the present tense, but when you give a command we use HABLA for the 2nd person, which is the imperative tense. That´s why you keep seeing and hearing "Hablame" because it´s the correct way to ask someone to do something (talk to me) in the imperative affirmative.
On the other hand, the "me" pronoun" in the other conjugations go before the verb: tú me hablas (you speak to me).
I hope that was helpful,
Best,
Rocio