Recently I've being playing some IL-2 1946, and in this flight simulator jet engines had a strange problem where if I suddenly throttle up more than 60% the engines would catch on fire. Is this a real thing? The engines that this happens on are the Jumo 004 and the BMW 003 on the Me 262 and the He 162.
Yes indeed. For the Jumo 004:
[A] shortcoming of the engine, common to all early turbojets, was its sluggish throttle response. Worse, it was fairly easy to inject too much fuel into the engine by throttling up too quickly, allowing heat to build up before the cooling air could remove it. This led to softening of the turbine blades, and was a major cause for engine failures.
To avoid rapid movements the levers of that era (and still being used on some types) had a friction setting that can be increased on decreased. High friction results in more force required to move the thrust lever.
Advancements in the hydromechanical units and the introduction of engine control units made controlling a jet engine much easier.
I remember reading (but I can't seem to find it now) that Frank Whittle had problems shutting down one of the early jet engines he worked on. It would just keep running and speeding up.