The word used does not do a good job of conveying what was probably intended.
Both quickest and fastest are comparative terms which imply that speed or velocities are being compared. That is almost certainly not the case here. While it is possible that actual speed at the time of finishing is being measured, it is far more likely that what is being compared are durations.
"Finished quickest" or "finished fastest" may be a good choice for something like 1/4 mile drag races where a high speed of the vehicle at the end of the run is valued - as well as the lowest elapsed time.
Here, most people will understand that the intended meaning is (probably)
"finished sooner than" / "finished before" / "was first" / "finished first" etc.
"My supervisor reported that I finished
much sooner than
all the other trainees in that period."