Rear gear swap for mustang?

I'm getting new differential gears installed on my 2014 ford mustang, the shop said they can adjust the speedo but I'm wondering would if have to get the car tuned as well. It has an automatic transmission and don't know if it will act up because of the new gears.

You don't need a tune just for gears. The speedometer/odometer is actually electronically controlled. Changing the settings so that it reads correctly after changing the rear end gears isn't a big deal. It can be accomplished with a hand held tuner or a computer, the ship more than likely has a computer they can adjust it with.

The gears the factory installs in vehicles are directly correlated to get the most out of the engines power curve. If you go changing the gears, you potentially throw off the power curve of the engine and not get the most out of it which could in fact hinder performance rather than increase it.