After finishing my Gnat course, I held for a while waiting for the pre-TWU Hunter refresher course. One day I went flying with a new QFI who had come from a non-FJ background. His flying was aggressive and not that good, to my inexperienced eyes. After a session of aeros, he had no idea how to fly the normal TAC dive procedure to Point Alfa, so I had to talk him through it....
Once back in the visual circuit, he exhorted me to pull to the buffet when turning downwind "otherwise you're not really trying hard enough"
I didn't go flying with him again and it didn't surprise me when he had a landing incident a few weeks later, badly damaging the aircraft.
Another non-FJ QFI killed himself and his student after mishandling the Gnat at Shawbury.
But a third pilot (ex-Victor), going through CFS to the Gnat, had the good sense to ask for a posting change as he felt that the little jet was too much for him.
It strikes me that it's those who feel they have something to prove, having never flown a FJ beforehand, who need to be watched the most when instructing on fast jet trainers. Maybe the ex-FJ pilots have a stronger sense of self-preservation?