As usual lots of really informative stuff on how things work
Of course a couple of layers below the introductory stuff might be the answer to the original posters question, which has to do with the variations in timing of the on-off event (mostly the on).
In my simplistic view it looks like
1. Turn on the ignitors
2. Turn on the fuel
3. Allow the fuel to stabilize its spray pattern in the engine exhaust air
4. Sense the light-off (pressure/temperature/N1) adjust the nozzle for optimum pressure/N1
The design keys are
powerful ignitors
Spray Nozzles
Flame holders
The system keys are the feedback loop that monitors pressure/temp/N1 against the nozzle position (either open/closed or variable)
The answer to the original posters questions versus altitude might indeed be a function of the time that it takes to achieve the desired spray patterns (feel free to add/correct my simplistic views)