Damage Control is an assigned duty during General Quarters only. Men assigned to DC parties are from the normal working divisions from the Engineering Department which includes A division, M division, B division, E division and R divisions.
Each individual within these divisions has a normal "day" job depending on their rating and the responsibilities of that division (always fixed). Again, they become part of a DC party ONLY during GQ. The deck ratings would handle things like the guns, lookouts, bridge functions (helmsman, engine order telegraph), ammunition handling, etc., during GQ. They would not be part of a DC party.
I've not served aboard submarines, and believe there is more cross training than the surface fleet, but ratings are ratings and division are divisions all with specific functions to be served during a normal non-combat watch and during General Quarters.
Actually, speaking of watches and such, there are two basic functions served by every sailor. One is his normal day job which starts at 8:00 and ends at 16:30 (hours as I recall from many years ago). A normal day job might be anything from airconditioning maintenance to boat maintenance to deck ape duties like painting and general ship maintenance.
Each sailor also has watches based on sections. These watches have nothing to do with a day job though there is some relation based on the responsibility of the division and the ratings within that division.
Typically, there are two 4-hour watches to be served during a 24 hour period plus the normal working day. At least one watch will fall - in whole or in part - in the normal work day except on Sunday's which is a day off except for watches.
Maybe you Richover boys can shed more light on how the pig boats are run. I can't image it is all that different than the surface fleet.
Anyway, with that said - and though it's not realistic - I just fill up my DC party with the best guys I can afford to get before leaving on patrol. That seems to work okay (I guess

).
Don't know if this means anything to anybody...and sorry for all the rambling as I try to recall details from my Navy days - which I really didn't care for anyway (computer simulations are much more fun)