You can figure this out by putting men (with different skill levels) in the compartments. The green bar will go up or down, but that takes 24 hours, because all skills, specializations etc. interfere.
I have the same question. In general I use some rules of thumb, yes that sounds pretty accurate
The first one is relatively easy, but the rest...?
Control room: Leadership (Watchman, Electrical?)
Engine room: Mechanics, Electrical
Torpedo room: Mechanics, Guns
Bridge: Watchman, Leadership
Guns: Guns, (Mechanics, Watchman, Leadership?)
Radio room: Electrical, (Watchman?)
Repair team: Mechanics, Electrical
There are some threads about this, but still I don't have a useful overview.