You do if you are tuning for performance
And a more advanced spark.
You contradict yourself.
You design it for a target octane rating. Yes. You lower the mapping for lower octane. Yes. so its NOW designed for the lower octane fuel!
I(f it has auto mapping it will definitely be better on the higher octane. If not, its pretty LIKELY but not certain that it will be
What does of course happen is that if its running rich because the fuel has more carbon in it - typically with aromatics, it will be leaned out by the ECU so it will do better mpg on higher carbon content fuel.
As I said, its not that simple.