I don’t think there is enough context to know exactly what it means. I think the second meaning mentioned by Diana makes more sense to me. When I first read this, I felt like they were arguing before this exchange. “A“ is trying to tell B to mind their own business and “B“ is saying “it’s on“ to indicate something is about to happen, an argument or physical altercation for example. In the US, one might say “it’s on“ after being challenged by someone else. Example: a: I bet you can’t finish that plate of food. B: oh, it’s on.