There are still many competing theories when it comes to the relationship between the Byzantine Thematic system and Military Lands. In my opinion, the two most convincing are the following: First, the belief that sometime in the seventh century, the Byzantine government distributed imperial lands to its soldiers in an attempt to allow them to support themselves while reducing monetary compensation (wages); The second, that during the seventh century, Byzantine armies were settled in the territory that would later become themes, supported financially and logistically by the local populations. Over the next several centuries these soldiers slowly acquired land in the territories they were settled.

I know these two stances may appear similar on the surface, but there is a clear distinction: in the first, lands were distributed to soldiers in exchange for service; in the second, soldiers are supported by the local lands, but their acquisition was not centrally mandated and happened organically over a long period of time. Either way, this relationship between soldiers and their lands was written into legal codes in the tenth and eleventh centuries, but we do not know if these laws were simply an official recognition of practices already going on, or an attempt to modify the existing system.

Let me give a quick overview of what we do know. In response to the Arab invasions and Byzantine defeats of the seventh century, the various field armies of the Byzantines were withdrawn from Syria and all territory south of Syria. These armies were settled at first in eastern Anatolia, likely in districts based on the land's ability to support the occupying soldiers. Over time many other districts were created in a similar fashion all over the empire, and the thematic system was no longer exclusive to Anatolia. By the 670s we start to see Byzantine seals, used by the state warehouses and arms suppliers, bearing the names of the themes, rather than the previous provincial names instated by Diocletian in the late third century. The next few hundred years are commonly referred to as the Byzantine Dark age, in part because of the lack of written sources that have survived. We don't know much about how the thematic system evolved through this period although the seals used by state warehouses continue to show up in archaeological finds and I believe we have at least one seal for every theme that we know of. The written sources improve in the ninth and tenth centuries and we begin to see laws specifically referencing soldiers, themes, and military lands. Most legislation centers around growing strain on the thematic system, specifically between the soldiers, or holders of the strateia (military obligation to the state), and the dynatoi, who are powerful provincial land owners. The cause of the conflicts focus on a growing trend of the dynatoi buying up lands owned by soldiers, or in some cases, local stratiotes (holders of strateia) willingly giving their land to their local dynatos to avoid taxes and other obligations. The dynatoi were not subject to tax or military service, so the increased consolidation of land under these land owners robbed the state of financial and military capability. The laws of Nicephorus II, Basil II and the other Macedonian emperors, dictate the strateia is to be non-transferable. In other words, the stratiotes could not sell or transfer their lands to individuals outside of certain categories. The categories are essentially limited to close family members and would exclude all dynatoi. These laws were also retroactive, if land with associated strateia was sold to the dynatoi, it could be repurchased at a reduced price by the stratiotes or his family. After these laws were enacted the only legal transfer of stratiotic land to a non-family member was if the possessor of the land could no longer meet their obligations either by providing an adult male for service, or commuting the obligation in cash or in kind (cash equivalent of grain for example). In this case, the state could transfer the lands and strateia to another family or individual.

Regarding the fulfillment of tax obligation while on campaign, your assessment is conflating a few different legal mechanisms. There did exist, among the civilian population, the practice of tax assessment by area or region so that even if some of the land had fallen out of use at the time of assessment, the community as a whole was still responsible for paying taxes based on the productivity the empty land would have had if it was in use. As far as military obligations or strateia, the soldiers were actually exempt from most taxes and so would not have been involved in this type of tax obligation. As far as keeping land productive while on campaign, this task either fell to the family or relatives of the soldier if they were poorer, or to tenants, slaves, or servants if the soldier was more wealthy. For example, five pounds gold would have been able to acquire land of roughly 720 modii, or 144 acres. We have some sources that indicate in Macedonia during the middle Byzantine period, a peasant family might live off 50 modii, and a poorer family might work a farm as small as 25 modii. Based on these statistics, a cavalryman with the recommended amount of land as dictated by Constantine VII (five pounds of gold worth) had land that could sustain as many 30 peasant families. Marines of the imperial and thematic fleets possessed land that could sustain as many as 20 peasant families (about 3 pounds of gold). While many infantrymen could be, and likely were, much poorer, we don't have the evidence to indicate their recommended land allotments. My point is that many soldiers weren't poor peasants, they were an elevated social and legal class above their civilian peers and many likely had help to work their lands while they were away on campaign. As for soldiers without such help, it was up to each local Strategos, or thematic general, to select soldiers who were in the best position to serve based on the needs of the planned military action. Poor soldiers who could not leave their land without suffering economically, were generally not called up, and could instead commute their service either fiscally, or via donations in kind (food or supplies).

As far as the law you are referring to, there is no evidence that extra lands were confiscated, or assigned to these new heavy cavalrymen of which there were very few. As few as 300 in a field army. Instead, the individuals who could already support the equipment, supplies, and horses associated with such a battlefield role, had their private land incorporated into their stratiotic land, and as such the land became associate with their strateia, making it inalienable, and exempt from certain taxes.

This is shorter than I wanted it to be but I'm writing this on my lunch break :). I hope it was helpful.

Sources

Byzantium and its Army Warren Treadgold

Warfare, State and Society in the Byzantine World John Haldon

Recruitment and Conscription John Haldon

Military Service, Lands, and the Status of Soldiers John Haldon