You will find, that on a faster transient test (i.e a lower gear) the turbo will spool later. Taken to the extreme, an engine dyno (steady state) the turbo will spool earlier.
If he ran it in 4th, you'd find your torque will increase.
Regarding the correction factor, this is applied due to ambient conditions when on test, mainly influenced by atmospheric pressure and air temperature. This is high at 15% i.e if your car made an observed 100bhp, with that correction factor the DIN 70020 corrected power would be 115bhp.
I would ask him if the figures are observed, corrected, and at the wheels (hub dyno can still calculate transmission loss too)
I suppose it's all irrelevant if you don't like how it drives though