There is actually a simple reason, it's because of the Tetrarchy. As described in that thread, the Roman emperors (or the imperial families even) had, up until 284 AD more or less kept up the image of there being a res publica with a princeps or First Citizen at the top of the status ladder. That changed drastically when Diocletian became Augustus in 284 AD and reformed both the administrative and military systems in the empire.^1

So, what was the Tetrarchy?

The Tetrarchy (the First Tetrarchy actually) is a system put in place by Diocletian to ensure a more secure ruling of the empire after a century of trouble. All since the assassination of Commodus (with the exception of Septimius Severus) the empire had been in the hands of whomever had the control of a large of part of the army at any time - or, as may be more true, by the Praetorian guard. Also Diocletian was one of these emperors; at the head of the Numerian protectores he saw the flaw in the non-existing system and brought about a rather sudden change, which however did require him beating his rival Carinus in 285 AD.

The Tetrarchy meant in practise that the empire was split in two halves, with an Augustus ruling the Western half and another Augustus ruling the Eastern half. They were both to resign after 20 years of ruling and would then be replaced by the two Caesares, each assigned as a sort of prince to the respective Augusti. And here is where one of the more clear changes to before shines through and puts a stop to the Principate in our modern eyes. Never before had there been a clear successor to the throne, now there were two. Of course, Augustus had spent basically the last 35 years of his life trying to find a successor. Marcus Aurelius was succeeded by his son Commodus. Septimius Severus left the empire to his sons Geta and Caracalla. However, none of these were actually proclaimed successors to the imperial throne, but merely implied as such because the princeps had decided so.

Was it a sudden change or a gradual one then?

Both! As described, the changes made by Diocletian were sudden, but his changes were not the only ones. Personally, I'd give the more concrete start of the reforms to Trajan Decius (r. 249-250 AD), and his successors, where Diocletian became the culmination point. It all goes back, as so much in the ancient world always seem to do, to religion.^2

The predecessor to Decius, Philip was in favour of Christianity and seemingly a rather popular emperor - in Rome. However, rebellions arose in some of the more remote regions which eventually led to Philip being beaten in battle by the general who was sent to crush these rebellions; they had instead proclaimed him emperor. Decius quickly added the name 'Trajanus' to his name, after one of the most (if not the most) popular emperor in Roman history - Trajan. Philip may or may not have been the first Christian emperor (Constantine is of course declared to be the first, some 50 years later),^3 but it doesn't matter here, because what is important is that he wasn't devout to the old gods. There was this sentiment in the empire at the time that all the bad things that had happened over the previous ~70 years and continued to happen, were because the gods were angered, and Decius was a good man to solve that issue.

In order to ensure the happiness of the gods it was important to keep sacrificing to the genius and numen of the emperor, and that all (according to Decius) citizens did so. You see, Christians did not sacrifice because it was against their religion to recognize the emperor, and so the gods were angered. Thus Trajan Decius put in effect one of the most infamous decrees in Roman history, which essentially said that:

[...] all inhabitants of the Empire [must] sacrifice to the gods, taste the sacrificial meat, and swear that they had always sacrificed.^4

On top of that, all sacrifices were to be registered with the authorities in order to prove that all citizens in fact did sacrifice. This led to a whole new business showing up where people could pay others to sacrifice in their stead, but that's a different story! To refuse to sacrifice could lead to things such as exile and loss of property, or even torture and death. Apparently, the only people exempted from this were the Jews.^5 Similar persecutions continued under Valerian, Diocletian, Galerius and Maximinus.

What all of this really ends up in is power. With everyone in the empire being forced to, and even supervised in, sacrificing to and worshipping one man, a significant change in the imperial structure can be seen. Up until the reign of Decius (starting with Julius Caesar and Octavian), worshipping the emperor^6 had been a voluntary practise, mostly overlooked and excercised by local municipal or regional priesthoods in the provinces. Decius decree on the other hand, was universal in the empire. It is why I argue that this is the first concrete starting point to what would eventually lead to the reforms of Diocletian and subsequently Constantine, which put the ruling emperor(s) at a more defined monarchial position.

Would the ancients have recognized the Principate and the Dominate, or is it a construction by historians?

Historians such as Tacitus and Suetonius recognized already at the turn of the 1st/2nd century AD that they were living in a different system than the old res publica. It would therefore be rather safe to say that people also in the 3rd century would be able to see that the imperial power centered more and more around the position of the emperor. The terminology however, is modern and is put at 284 AD because of the introduction of the Tetrarchy, which eventually would lead to the (also modern construction) separation of the Eastern and Western Roman Empire. Constantine did actually re-unite both halves of the empire during his reign, but by the end of the 4th century, the empire was de facto an absolute monarchy.^7

---

[1] Le Glay, Voisin & Le Bohec, A History of Rome, p. 473.

[2] The actual starting point of what would eventually lead to the Dominate can be discussed, but I've chosen Decius because of the implication of his severe decree. Religion played a large part in ancient life, and by the middle of the 3rd century AD, Christianity had grown and rivaled paganism in the empire.

[3] Rives, J.B. (1999), "The Decree of Decius and the Religion of Empire" in The Journal of Roman Studies, vol. 89, p.140.

[4] Rives, J.B. (1999), "The Decree of Decius and the Religion of Empire" in The Journal of Roman Studies, vol. 89, p. 141.

[5] Rives, J.B. (1999), "The Decree of Decius and the Religion of Empire" in The Journal of Roman Studies, vol. 89, pp. 137-138.

[6] I just want to point out that I by no means recognize Julius Caesar to have been an emperor. It's a semi-frequent question on the subreddit and I don't want there to be any confusion. He is the starting point of the Imperial Cult though.

[7] Le Glay, Voisin & Le Bohec, A History of Rome, p. 502.