I disagree with that. The House of Gaius has ruled for 1,000 years and while a Cadet Branch might have taken over, as we know the House isn't all that fertile, I personally doubt they simply started over, if only because it would have been an insult to the original Primus.
At the very least, there has had to have been over 20 First Citizens of the House of Gaius in my estimation. I would say that the average reign has been for approximaely years, inheriting about age 25, giving them 25 years to have a son, then 25 more to let him get old enough to rule. Actually, my average is probably wildly overstated so there has probably been a lot more First Citizens than just 20.
Most likely the original Primus got the name when he took over and began to rule as First Citizen. It might have been that he shared the same real name as his son, so people started talking about him as Gaius Primus to differentiate between him and his son. Therefore the likelhood is that the numeration became used for the really Great first citizens and Sextus took it for his own.
As for when the Romans who became the Alerans arrived, Jim had pinpointed it fairly accurately, during the reign of Gaius Agustus Caesar, also known as Octavian/Octavius which is the supposed base for October. Augustus never took the title of Emperor although he held the power. He always insisted upon the title of 'First Citizen', can you see the parallels.
The organization of the Legions is pretty much the same as during Augustus reign. The only real question is where all the nice horsies came from since generally the only horses in a camp would be for the officers and most transport was by mule or oxen wagon.