I suggest not to use auto-tune. In my opinion this function is poorly implemented by the ArduPilot developers.
I think it can’t work even theoretically and the chance that the results will somehow work is as high as the chance that the copter will behave either too sluggish or too responsive. This is because of the fact, that auto-tune modifies two PIDs at once, not caring about the fact that the user input has to be considered as well. As the desired attitude is the difference between the user input and the current attitude. Unfortunately, it just checks overshoot and stabilization, not the response towards user input.
After getting miserable PIDs you need to change the values in the All Parameter Tab. I also had this kind of problem.