You and the well driller must have skipped physics class. If he put 40 pounds of air or 10 or 50 into a plain tank, when the pump shut off at 60, that AIR was at 60 also. You must have a very special and humorous chinese pressure gauge.
Well pro? I don't think so. If so, it must have been his first job.
Pressurizing the tank with a compressor to the CUT IN pressure is fine. [not so fine if he left the air release valve in] When it shuts off it will be at shut off pressure. Period.
But water loves air, and you will be doing this more like every month at the very least. You can replace an airmaker on the surface, however. The overpressure from the compressor gives you MUCH more drawdown, however.