The nuts should be checked with a torque wrench after about half an hour stationary or after approximately 40 miles driving.
The garage should do it for you in either case.
the gun would have the correct torque setting so assuming it's working it should be fine but being a bit OCD about nuts and bolts i would always check myself if i don't see the fitter do it. To be fair though my local tyreland always put the manual bar on them anyway.
working in the trade our guys have high end air guns but they still check with a proper torque wrench, wouldnt trust an air gun anyway all our torque wrenches are numbered/ calibrated/checked by an outside company every 6 months, they DONT calibrate air guns. You are more in danger of over tightening than under tightening we have 3 BMWs here that have had nuts 'gunned up' we are still trying to remove them, and yes we have all the high tech kit to do it but still struggling...
Most air guns will tighten much stronger than a person, my garage always lets the owner tighten a wheel with the brace. As they point out what do you do if you're in the middle of nowhere and can't undo the nuts to change a wheel.