About 2500 years ago. In fact, the Greeks started portraying tyranny as a universally negative and hated thing pretty much immediately after the early tyrants your textbook told you about.

In his brilliant article 'Before turannoi were tyrants', Greg Anderson showed that "tyranny" was not a negative term when it was adopted into the Greek language, probably from Lydian, in the 7th century BC. The earliest attestation, in a poem by Archilochos, seems to take the word to mean simply "great power" or "great wealth" - both of which were seen as desirable and admirable by Greek elites at the time. It seems tyranny was generally regarded as the prize at the end of the endemic factional competition for power and influence that marked the political life of early Greek city-states. As you say, the early tyrants are generally not known as despotic, oppressive rulers; several are remembered by tradition as champions of the people, who overthrew old leisure-class oligarchies, curtailed the power of greedy rivals and treated citizens to many benefactions. For example, all sources agree that Peisistratos of Athens, who ruled about 546-527 BC, ruled in accordance with the existing laws and adorned his city with temples, fountains and festivals. According to a student of Aristotle, his rule was remembered by the Athenians as an "Age of Kronos" (i.e. a golden age of fertility and prosperity).

Tyrants, however, represented the monopolisation of power in a system of rival factions; they often seem to have tried to make their position hereditary. In the more stable tyrannies, the sons of tyrants often succeeded to the position. These sons were rarely as well-regarded as the "first generation" of tyrants; it seems that Greek communities were perfectly happy to see a tyrant rise to power, but could not tolerate the notion of power remaining forever in the hands of one family. Possibly this is related to the idea that those rising to the tyranny in a context of elite rivalry must have been men of some political skill or military power, but those who simply inherited the position did not need to be men of any particular ability. However this may be, tyranny may have been a common form of government in Archaic Greece, but it rarely lasted more than two generations before being overthrown. Knowing this, successor tyrants were more likely to act aggressively to assert their power, which in turn increased the likelihood of inciting rebellion.

The Athenians maintained that they were liberated from an oppressive tyranny when two lovers called Harmodios and Aristogeiton assassinated Peisistratos' son and successor around 514 BC. The so-called "tyrant-slayers" became a rallying point of the young democracy; songs were sung to them, statues made, and honours were given to their descendants in perpetuity. However, inquisitive Athenians knew perfectly well that the story was false; we only know its details today because Herodotos, Thucydides and the aforementioned student of Aristotle all explain at length what they discovered about the actual situation. Harmodios and Aristogeiton, they say, were not enraged by the tyranny at all, but were simply involved in a lovers' quarrel. They may have plotted to murder both (or all 3) of Peisistratos' sons, but they attacked in haste and only managed to kill the less capable Hipparchos, leaving the true tyrant Hippias in charge of the city. Only then, driven to paranoid fear by the attempt on his life, did Hippias begin to rule with an iron fist. He had many citizens exiled or executed and generally seems to have inflicted a reign of terror on Athens in the hope of rooting out a non-existent conspiracy. Prominent Athenians like Kleisthenes called on the Spartans to intervene, and in 510 BC, Hippias was finally driven out. A few years later, Kleisthenes initiated the reforms that are regarded as the foundation of Athenian democracy. But the relevant question is: was Hippias always a hated despot, inspiring plots like that of Harmodios and Aristogeiton? Or was he hated only because of his violent reaction to the tyrant-slayers' attack, ironically inspiring Athenians of later generations to worship Harmodios and Aristogeiton as liberators?

Unfortunately, it's hard to give a definitive answer, because this example is by far the best known, and it still remains largely hidden in the murky depths of Archaic Greek history. But the shift in attitude towards tyrants seems to have been a general feature of Greek political thought towards the end of the sixth century BC. It's at this time that Sparta makes a name for itself by going around deposing tyrants in states as far afield as Samos (and Athens, as noted above). From this time onward, tyranny is never again regarded even as morally neutral. It is always portrayed as evil, and becomes more so as the centuries pass. Fear and hatred of tyranny is a defining feature of Greek thought throughout the Classical period, and many features of Greek democratic government (magistracies filled by lot for short periods; administration by panels of magistrates and generals rather than single leaders; the institution of ostracism/petalism, by which the people could vote to send a chosen citizen into exile) are clearly intended specifically to prevent any single person from gaining too much power. Anyone who managed to gain prominence in politics immediately attracted suspicions of aiming for tyranny. Athens issued decrees to the effect that anyone caught plotting to establish a tyranny could be killed with impunity, and that all Athenian citizens were to swear that they would do so without hesitation. The writings of authors with more oligarchic leanings, such as Plato, Aristotle and Isokrates, show clearly that tyranny was hated by democrats and oligarchs alike; the latter may have argued that democracy was blind, lawless and unstable, but they showed that the same was true for tyranny. Even though one-man rule was on the rise in the fourth century BC, and some of the Greek world's most powerful political entities were intermittently run by tyrants (notably Syracuse and Thessaly), it seems to have been all but universally agreed that this was a bad thing, and that each of these states craved liberation.

Later centuries built this indignation at the concept of tyranny to ever greater heights. Fourth-century tyrants like Dionysios of Syracuse became archetypes of the evil tyrant: men whose insatiable desire for power reflected their insatiable desire in general, and who were characterised by violence, wrath, greed, arrogance, gluttony, dishonesty, distrust, sexual perversion, and everything else that the ideal citizen would keep far from him. Greek and later Roman thought portrayed the tyrant as the anti-citizen - someone whose unrestrained appetites made it impossible for him to live a good life within the confounds of civil society, regulated as it was by laws, customs and traditions. From the mere exponent of socio-political processes, the tyrant had become their worst abberation.

Whence the change? I've already noted that tyrannical dynasties rarely lasted long, and that there was probably some sense that one-man rule wasn't right even before the Classical period. This may well have been the product simply of rival factions wanting access to power; one reason for the success of Peisistratos' tyranny was that (as epigraphic evidence shows) he seems to have been able to co-opt other members of the elite in his system as long as it was understood who was really in charge. The process of tyrannical coups and their eventual violent overthrow also may have given tyranny some nasty associations with instability and even civil war, leading Greeks to seek to establish more stable systems of government.

But it seems likely that it was the increasing sophistication of Greek states and their institutions, and the accompanying growth of civic consciousness, that made tyrannies increasingly unpalatable specifically in the later sixth century BC. As ideas like citizenship, equality, and the rule of law became rooted in Greek thinking about political communities, it would have seemed increasingly absurd to them that one man should be able to do whatever he wanted to the rest. The arrival of the Persians put the final nail in the coffin of tyranny; Persia, ruled by a monarch itself, often used local tyrants as their loyal governors, increasing the Greek distaste for this unaccountable form of rule. As they developed systems that were more inclusive, more accountable, and more stable, they started seeing tyranny not as a feature but as an abberation, and eventually came to think that even murder was justified if it helped to get rid of them.