In fact, by the period of the game, neither Rome nor any other country, AFAIK, had prison as punishment. Criminals were put to death, sold to slavery or send to exile (the upper classes). By then, to be forced to live out of your town or your country was a very harsh punishment, as out of your country you wero no longer a citizen, so you have very few or no rights at all.
The Tullianum was used only as a very temporary prison, prior to execution. By the way, at the time it was a hole in the ground, without doors, and prisoners were taken there by a ladder ... or simply dropped.