Ideally, the mechanic should've ridden the bike in the small chainring and all the cogs in he back, dragging the rear brake and putting maximum torque into the bike to see if it would skip, and then testing in the other two chainrings in the biggest cog. In the case of your bike I probably would've recommended a new cassette and all new chainrings--depending on the price, its sometimes more economical to replace the crankset entirely.

In this case its almost certainly a worn cassette. The Shimano chain is an upgrade.