Hello! This is a great question. Part of the delay in the release of the Auran Empire setting is that I'm still working through some of these issues, including how much complexity offer and how closely to show how the math of the domain rules links to the governance structure.
In general, the technology of the Auran Empire setting should be understood to encompass the very best knowledge of Antiquity plus some but not all of the pre-gunpowder developments of the Middle Ages, including stirrups, lenses, hourglasses, horse collars, and horse shoes. I have been inspired by archeological finds such as the Antithekyra mechanism to create a setting that is quite technologically advanced (relatively speaking).
The primary advantage of the heavy plow was that it allowed the soils of central and northern Europe to be farmed more effectively, so it has little impact on the Mediterranean vistas of the Auran setting. I would say that it is probably available to Auranized settlers, but that the northerners beyond the Jutting Mountains are less advanced. So there has not yet been a large agricultural advancement outside the Auran areas. You can reflect this in your campaign by increasing or decreasing land values in areas of the map.
Governance of the Auran Empire was inspired by that of the Byzantine Empire (hence "Exarch" as the ruler of a province). The Byzantines relied at various times on a semi-feudal system, first under the themes then later through the system of pronoia, and likewise the Auran Empire is semi-feudal.
The country folk of the Auran Empire can be compared to Byzantine peasants or Roman colonoi. They are not slaves, as slavery is outlawed in the Auran Empire, but they may be indentured servants, or families which include some indentured and some non-indentured servants. As in the Principate, however, citizenship can be acquired through military service.
In terms of administration, the Tarkaun (emperor) appoints exarchs, who in turn appoint subordinate magistrates, all the way down the chain of vassalage. Technically these appointments have to be approved by a council of the leading families (the Senate in Aura, and lesser counciles down the line) but de facto the military vote is what matters.
The magistrates are empowered to collect rents from the territories under their control, but have a responsibility of funding the military force of the empire either directly (hiring troops) or indirectly (paying funds for troops that are sent elsewhere). The magistrates are also responsible for civic expenses (festivals) and religious liturgies for the local temples (10% tithes). Magistrates maintain their positions with gifts and tributes to the superior magistrates who appointed them (the 20% tax).
The magistracies are non-hereditary but often a magistrate position will be de facto hereditary as an aristocratic land-owning family arranges to make sure that one of its members is always the magistrate in charge of the lands it owns. In theory the, aristocrat land-owners would be paying a rent to the imperially-appointed delegate, who then covers the government expenses, while the land-owners keep any surplus production for themsleves, but in practice they're paying rent to themselves and covering government expenses themselves.
In a circumstance where a magistrate is governing land he does not own, the magistrate would be entitled to charge a rent to the land-owner(s) set by the Emperor, and would receive gifts and tribute from the magistrates he himself appoints. In game terms, this rent would approximate 6-8gp per family. The magistrate would then be responsible for all the usual domain costs. In most cases, it's a wash but if the land was particularly valuable (high Land value) then the magistrate might be poorer than he would be if he controlled the land.
It is vastly simpler to assume the magistrate is the landowner of the lands he presides over, but the math works out either way.
For example, imagine a domain with 500 families, Land Value 8. It will generate (8 Land + 4 Services + 2 Tax = 14 x 500) 7,000gp per month. Assume it has 5 subordinate domains that yield vassal revenue of 5,000gp per month, or 12,000gp total.
The magistrate who runs this domain is responsible for stronghold upkeep (let's say 500gp); tithes (1,200gp); taxes (2,400gp - actually going as tribute to the magistrate who appointed him); festivals (2,500gp every 3 months, or 833gp per month); and garrison (2gp per family, or 1,000gp), or 5,938gp total. The remaining 6,062gp is his to keep, if he owns the land.
If the magistrate didn't own the land, then the math would be slightly different. The landowners would first earn 7,000gp per month. From there they would pay the magistrate HIS rent - which would be something like (6gp x 500) 3,000gp per month. The magistrate would then collect his tribute from his own appointed delegates of 5,000gp per month. The magistrate would then pay his expenses (still 5,938gp), leaving him with ~ 2,000gp. The landowners, meanwhile would keep about ~ 4,000gp.
(Note that the math above approximates the result that you would get if a passive landowner hired a henchman of appropriate level to run the domain for him, paying all expenses plus his salary.)
You can add complexity from there - a magistrate might be a landowner of Domain X but a ruler of Domain Y, etc. There might be many small landowners splitting the 4,000gp amongst themselves, or one large plantation owner. Etc.