I would think an a/c guy would have fixed the fans when he charged it...
Anyway,
..he is correct in the fact that the fan should come on when the high side pressure reaches switch cut-in pressure. [I think yours is 20 bar]
You want to look at the fuse first , the resistor wires behind the driver headlamp, and , just in case he did not check it, jumper the high pressure switch at the drier and see if you get fan ..
If not , you have a circuit problem, [fuse,relat,etc.]if yes, then you have a bad sw OR, he did not completly charge the system..[providing it is a warm.hot day, of course]
Gages are nice here, but a quick look at Eye Sight glass will tell if freon level
is adequate to trip fan pressure sw.
There is much info on a/c condenser fan operation in archieves..