One, if you do have air dont rev it - the coolant will foam, thats bad. To check, uses a 1/4" socket wrench and open the crossover tube at the front center of the engine. Its that black tube thats front and center, you may have to remove the "beauty cover" if installed. This is the ONLY place to fill the system. The overfill tank is an expansion tank, not a fill location.
The cap should be easy to get off since the mechanic would have had to open it recently to fill. If its hard to get open and its easy to see it had not been in a while, find a new mechanic please! And do this when its cool, or open VERY slowly.
Once open, take a peak. If you see air that your problem. Fill with coolant/water mix. Please do not use tap water. Once filled, replace cap and tighten just a little, it does not need to be very tight at all. Drive around for a bit, try to find an bumpy road or corn field - joking about the corn field. Wait for it to cool a bit and reopen, remove any additional air.
After three times you should be good to go, but I recommend checking it again within 30 days. Some air-pockets can "break free" and work their way to the crossover tube.
Please let us know if you find air and if this help. If you dont find air we will have to look elsewhere!
