The civil war of the 1st century BC was essentially a struggle between two groups: the optimates and the populares. Caesar, Crassus, and Pompey were essentially populares; the death of Julia in 54 and in the death of Crassus in 53 drove a wedge between Caesar and Pompey, who ultimately went over to the optimates.

The concept of three "factions"--especially gens based ones--competing amongst themselves to take control from the Senate? Utter nonsense. As are the names they've come up with; while the gens Julius or "Julii" was an actual gens, the creators obviously had little idea of how naming conventions worked. Scipio was not of the "Scipii" but instead of the gens Cornelius, and Brutus was from the gens Junius.

So, yes. A little weird historically speaking. It would make more sense--and be more interesting--to have one SPQR faction, and to have each "family member" have a loyalty either to the optimates or the populares. Then when civil war broke out, you could have two sides, instead of the ridiculous three-and-a-half factions the normal version does.

ADDENDUM: "Imperator" was a military title adopted by Augustus in order to take control of the Republic. It doesn't mean "Emperor" until much later, although the title was restricted to the Imperial family after the time of Augustus.