She's saying someone else will do something to them for their actions as a consequence, just like you are saying someone else will do something to her as a consequence. She's not saying she's going to do it herself, just like you're not saying you're going to do something to her yourself are you?
You said, "so don't make empty treats" in response to something happening to her. You're saying that if someone makes empty threats then something will happen. That's a threat of action.