Mechanic says not to use top three/bottom two gears or the chain will throw
You have a double front, right? The usual advice is to not shift into the highest 3 gears in the rear cassette when in front the chain is on the large chainring, and to not shift into the smallest 3 cogs, when the chain in front is on the small chainring.

This prevents cross-chaining, which wears the chain quickly, produces noise and difficult shifting. Furthermore, some derailleurs may not even support those extreme combinations, when the chain is crossed.

On a side note, the chain should not be dropping in any gear combination, probably the limit screws should be touched a bit, as linac describes.