Here are a few things you can check
- Do a compression test, confirm engine is healthy
- Check the timing belt has been timed correctly. If it's VVTI make sure you have timed the belt using the straight marks rather than the dots.
- If you have aftermarket cams/cam pulleys, check they have been shimmed correctly and cam pulleys are set to 0 (change only once tuning if needed).
- Check your throttle opens 100%. Sometimes it's possible that throttle system gets stuck on a nearby fuel fitting/fuel hose etc.
- If you are using VVTI ethrottle still, then make sure tuner has calibrated ethrottle map to give proper throttle opening. Take intercooler pipe off and check that throttle opens fully.
- Smoke/Boost leak check the car. You could have a major boost leak you don't know about.
- Check that your ignition system is new. New coilpacks, new coilpack clips, NGK Grade 8 spark plugs or colder. If not, could be experiencing a misfire.
- Check your VVTI system is working correctly, solenoid is good, filter is clean etc. Check that the map he has put in for VVTI makes sense. Generally VVT should be aggressive in low rpm's before tapering off by the time you reach high rpm.
- Check you have no exhaust blockages. Cats, broken exhaust backboxes, bungs etc. A blockage will lead to higher turbo backpressure strangling your power and causing excessive cylinder heat leading to early onset of det.
- Check alternator charging voltage, should be doing 14v on idle and around 13.5 on full boost.
- Also not that it should affect your total power output, but denso injectors are shit. Lots of drivability issues from them, especially when they get warm. Might want to put some bosch style injectors on your future wishlist.
- Check tuner has calibrated base timing on the ECU correctly.
If you have a map file, logs from the dyno and printout of dyno pull then I can investigate the tune further.