The Star Wars Wikia has an article that discusses Star Wars: Rebellion as well. On the subject of officers, it had this to say:
Some characters could be given military ranks by the player to put
them in specific roles.
An admiral increased a fleet's performance by
enhancing firepower, shields and speed.
A general increased the
performance of troops and reduced the likelihood of successful enemy
missions on a friendly planet.
A commander increased the combat
efficiency and speed of starfighter squadrons. Ship-based squadrons
also launch faster with a commander present.
While it also does not describe the mathematics behind which stats matter, nor the amounts by which they are enhanced, it does list the specific things that are enhanced (firepower, shields, speed, etc...).