Are glow plugs supposed to stay on after the engine has started to help with the firing of the first few revolutions?
Actually with modern engines, they can and do come on after startup. I think the reasons are spelled out fairly well in this article on Engine Builder Magazine:
The government wanted to reduce the amount of diesel hydrocarbons and nitrogen oxide levels being emitted from diesel engines. Now, this is where the importance of the glow plugs comes in. Not only do the glow plugs cycle to aid the engine during cold weather start up, but also after the engine is cranked – they will continue to cycle to reduce the amount of start-up emissions. This helps reduce the smoke that most diesel engines produce when being cranked on cold mornings.
To reiterate, they come on after engine startup to reduce emissions and smoke. The combustion chamber will not immediately come up to temperature after startup. It takes a while for things to get heated, like the heads, cylinder walls, and most importantly, the cooling system. Once these things are warmed up, emissions are where they should be and the glow plugs don't need to come on anymore.