Problem is rebels is not a very good word for them, but doomstacks, seeing as when there's a Civil War you will have 20 or so doomstacks appear in one of your provinces.
Rebels often only appear when your people are unhappy. Squalor and food are 2 of the major things that contribute to a negative happiness of your population. Depending on the strength of your provinces and armies 1 rebel army stack will spawn with a varying strength of 3-20 stacks. However the best troops they get are legionaries if I am not mistaken.
Oh and just FYI the Civil War doomstack spawns have got nothing to do with your people's happiness levels, squalor or food, and they get the best units available for recruiting in the settlement in which they spawned, simply because you are referring to actual Rebels while I was talking about Civil War "rebels" hehe
(what controls the doomstacks as seen here Link is controlled by the influences of the other political factions within your nation)
the number of doomstacks that spawn with civil war, is SUPPOSE to be based on senate power, squalor/happiness of entire empire, quality and number of units in each stack, is further determined by your tech/overall upgrades in your empire
But....as everything else, its bugged atm, and spawns random number of doomstacks, regardless of your power etc.