I would say they didn't follow the hot start procedure.
Over Primed it and managed to get fuel into the air filter.
More than likely 5 squirts with full mixture then waggle the throttle while cranking it.
The initial taxi will have been other issues.
But your right clueless instructor that doesn't have a clue what they are teaching or how to operate the aircraft. The won't be an airline op for starting a piston engine any more.