Who is selling this tune? They aren't throwing out emissions.
The only way you are saving fuel on an aftermarket tune is during WOT. Stock tunes are super rich compared to what a custom tune ends up at. Ford will dump 10:1 or more at WOT where a custom tune will be in the 12:1 range.
For the 99% of time you aren't WOT though- there are no MPG gains to be had.
I can see an aftermarket tune gaining MPG in something like a Focus ST that is driven in anger most of the time. They don't have a ton of power so you can run them WOT a lot. I drove one and I could floor it getting on the highway onramp, and keep it pinned for quite a while. You aren't doing that in something with 700+ HP- the amount of time you can spend with it at WOT is so small.