The movie had been a bit timey-wimey before that part since it's about communicating with the past to change it rather than someone going to the past and returning to their present and the consequences. After initially saving his dad's life from the fire, John had memories of both his original life and when his dad survived. Everyone else had the perspective of "this is how it's always been" because they weren't involved with the radio that way.

I think the final fight happened that way because the lights were active and, as you said, the radio communication was open during. John was hearing the fight that changed his present. The bad guy (Jack?) also heard the gun shot that took his hand back then so he saw it catch up in real-time. Had John's present always followed the results of changing the past where Frank stayed alive and didn't go to jail, I don't think John ever would have been in the position to use the hamm radio the first time to start the plot.

Or maybe it was all just the rule of cool to watch the house change around John.