A poppet valve has a spring loaded check valve function, so as the pressure changes, the valve actuates. The force of the spring determines the pressure it activates at. A typical hot water heater has a poppet safety valve, for example. the spray nozzels in the 250 series have a poppet that changes the spray pattern and volume during the start.
The time limit for most engines is actually kind of arbitrary, as it is a measure of how healthy the start is. Long time usually means the flame pattern is bad, (dirty nozzles?) and things are not normal.
There is a starter motor limit, but usually it is a problem only if there is no lightoff, and the starter could overheat itself. The light starter motors that helos use are not beefy enough to absorb all the heat of a continuous cycle at full rated power, but they don't have to be if we respect their duty cycle ourselves. That causes the on one minute-off one minute-on one minute-off 30 minutes timings that most flight manuals have.