I would argue that modern military logistics didn't evolve from premodern forebears. Rather, they were the product of a radical break with the past. Systemic, rational organization was applied to logistics for much of its premodern history; the cause of this break was rather to be found in the nature of modern supply requirements.

There were important continuities in logistical systems up to the beginning of the twentieth century. For most of history, the largest requirements of an army in terms of weight were water, fodder for animals, firewood, and food for men. The chief means of transport for armies into the Second World War was the wagon, drawn by oxen, horses, or mules, or else pack animals, which themselves needed to feed. Their ability to move bulky supplies overland was limited by the increasing share of the cargo needed simply to feed the animals drawing the load. Since the wagon owners were often private merchants seeking a profit by conveying supplies, and they only got paid for what they delivered, moving provisions even well short of the theoretical limits was often not economically viable.

Moving supplies large distances overland, though, was often not necessary for armies prior to C20. The needs I enumerated above are likely to be found in relative abundance in any populated area; a farming village would try to keep a year's worth of food stored, in case of a harvest failure, and a year of food for 30 people is a day of food for 10,000. Larger villages and populous towns offered even more to an army. Since overland transport was essentially impossible, and almost all an army's needs could be met by the seat of war itself, the obvious and most widely employed solution was to take everything the army needed from the theater.

If moving supplies to armies was hard, moving armies to supplies was relatively easy; this is the system employed by Xerxes, Alexander the Great, Hannibal, Louis XIV, the Duke of Marlborough, and Napoleon. Often, this was accomplished by cowing the local authorities with threats of punishment [hostage taking, burning property and people], or by offers of gifts or payment, or a combination of the two. The food and fodder would be collected ahead of the army on its line of march and picked up where it was. There are many variations to be made, but the core of the system was to draw one's supplies from the area immediately about the army.

When campaigning on enemy territory, this had the double virtue of sustaining one's own army and damaging the enemy in the same stroke. Onasander in this passage merely codifies what every general of his age already knew. Often, armies would collect tax records from local magistrates and use these as the basis for apportioning their demands through the territory. In turn, a state would often waive the right to collect taxes from a community that had payed its allotment to an occupying enemy, lacking the political capital to demand that kind of sacrifice; the state had failed its duty to protect them from foreign depredation. For Frederick the Great, at least a third of the cost of the Seven Years War was wrung out of enemy territory.

The real difficulty in supplying an army came not when it was on the move, but rather when they had to stay still. When operations paused for winter, armies usually dispersed into quarters so each house only had to feed one soldier. When they were in full swing, though, sustaining an army in one place through a siege put armies to the ultimate logistical test. Having no need to move, fortifications can store up immense quantities of supply in advance, and with the power of walls, they can make do defending with fewer mouths.

There were two main ways around these advantages; leverage the greater force available to the besieger to capture the place before supplies run out, or try to arrange so the defender runs out of supplies first. The first usually meant taking the place by storm, building engines or other works to capture the walls, open the gates, etc. The second way meant establishing true supply lines; this was most practical when the army was campaigning near a navigable waterway, as ships, boats, and barges have a vastly greater range than animals. While stocks were being built up, the besiegers would do all they could to strip the surrounding territory of food and fodder and so buy themselves more time.

The advent of gunpowder, transformative as it was in so many respects, did little to change the logistics of armies. Most campaigns lasted no more than 180 days, and in that time, it was common for no battle to be fought. If a battle or siege was part of the campaign, though, the weight of ammunition consumed always paled in comparison to the food and fodder an army needed, and most had little trouble simply carrying all the ammunition they would need for the campaign from the beginning. From the other end of the stick, not even railroads, with their incredible throughput compared to conventional transportation, allowed armies to do without local supply. They simply weren't flexible enough to keep up on the advance, especially since the rails into enemy territory were often commanded by fortresses.

The beginning of the 20th century changed all this. The development of rapid fire weapons engineered with precise tolerances, particularly quick-firing artillery, exponentially increased the weight of ammunition an army could throw at its enemy. Refined fuels for internal combustion engines also became more important. To put it bluntly, howitzer shells don't grow on trees, while in a sense the necessities of pre-modern war may as well have. They needed to be supplied from the army's base in the rear, conveyed forward by relays of railroads and vehicles; the further from base the army advanced, the more difficult the process became.

As a result, it became for the first time easier for an army to say still than to move. This change in the nature of supplies made it relatively more easy to wage war with powerful armies in previously inhospitable territory, such as deserts. This factor was crucial in the relative immobility of armies on the Western Front of WWI, especially as they were still reliant on horse drawn wagons to move supplies from the railheads to the troops. In the more mobile east, a definite limits still reigned in the effect of victories; exploitation/pursuit past 90 miles or so became extremely difficult, owing to the expenditure of so many heavy shells.

While the mass adoption of motorized transport has alleviated much of the mobility problems that plagued armies during the World Wars, we still live in the same era of military logistics, as military supplies become ever more complex and specific and correspondingly impossible to furnish from the theater of war.

I would recommend looking at, among others,

Donald W. Engels, Alexander the Great and the Logistics of the Macedonian Army

Jonathan P. Roth, The Logistics of the Roman Army at War

John F. Shean, "Hannibal's Mules: The Logistical Limitations of Hannibal's Army and the Battle of Cannae"

John Lynn, Feeding Mars: Logistics In Western Warfare From The Middle Ages To The Present

Yuval Noah Harari, "Strategy and Supply in Fourteenth-Century Western European Invasion Campaigns"

Clifford Rogers, Soldiers' Lives Through History: The Middle Ages

Molly M. Madden, "The Black Prince at War: The Anatomy of a Chevauchée" https://conservancy.umn.edu/bitstream/handle/11299/171443/Madden_umn_0130E_15639.pdf?sequence=1&isAllowed=y

Geoffrey Parker, The Army of Flanders and the Spanish Road

Martin Van Crevald, Supplying War

Carl von Clausewitz, On War, Book V, Chapter 14, "Maintenance and Supply"