I am not sure if they both mean the same thing, but if they don't mean the same thing is it possible that "talk back at you" implies a more aggressive opposition than "talk back to you"?
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"Talk back at you" sounds like a colloquialism. I assume it means more or less the same as "Talk back to you". – Andrew Apr 9 '19 at 5:15
Saying "talk to" implies a two-way conversation. Sometimes we want to make a point of saying that there was no conversation, and that one person was talking but not listening. In those cases "talk at" is used.
After talking to my teacher on the phone, mum came to my room and talked at me for half an hour about my "attitude".
I guess you could use "talk back at me" to mean "the person replied to me but didn't listen to what I said".
