Engi are naturally faster at making repairs. Does extinguishing fires count as a repair action?
My answer to your question is two-fold: it works on the output end, but not on the experience end. I watched the repair experience meter as my crewmember put out a large fire, and nothing changed. However, it does seem like their effectiveness at extinguishing it relies on that repair skill. In response to your edit, I would assume that yes, classes more suited to repairs are more suited to putting out fires. However, I have no clue if the Rockman attribute of stomping on fires affects this.