From memory, technology is calculated as a "tech cost" - every province you have contributes to the tech cost for each tech category.
Citizens in each province generates a number of "tech points" (for lack of a better term) each turn. Once you have more tech points than that level's tech cost, that category advances to the next level.
Government officials (Quaestors and such, or your country's equivalent) add a multiplier to this based on their Finesse value.
It's worth remembering that conquering provinces will turn most of their Citizens into Freedmen (and Slaves, IIRC), so conquest will not only increase the tech cost, but will not contribute to tech in the short term. If you ever want to conquer anything, make sure you take the Citizenship idea!
Hope that helps.
