According to the FAQ the Roman reforms take place when the following conditions are met by the Roman player:
Quote Originally Posted by Europa Barbarorum FAQ
Polybian
Spoiler Alert, click show to read: 
at least year 242, either hold 2 of these cities (Segesta, Mediolanum, Patavium, Bononia) AND 2 of these (Lilibeo, Messana, Syracuse) OR wait until 210BC
You get the new units after upgrading your Mic's. In settlements you don't upgrade you keep your old camillan units, and you are still able to retrain your old veterans.

Marian
Spoiler Alert, click show to read: 
At least year 172BC, have 6 Latifundia built, hold at least 45 settlements, fight more than 250 battles and have a character that is:

Intelligent/Charismatic/Vigorous
Popularis
Consul or Ex-Consul
Has Influence and Command > 2

OR just conquer 90 settlements.

Augustian
Spoiler Alert, click show to read: 
At least year 125BC, hold 90 settlements, have at least 45 type2 settlements, fight 400 battles, and a general that is:

Intelligent/Charismatic/Vigorous
At least Skilled Bureaucrat
At least Arrogans
At least Expert Recruiter
Can't be Selfless

If these conditions are met, the general will receive a trait telling he wants to seize power. Make him the Faction Heir and as soon as he becomes the leader the reforms will happen.
Edit: Kugutsu beat me to it.