Did some early jet engines catch on fire at higher power settings?
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.