This isn’t explicitly addressed in the films, but I think we can say that knowledge of vampires and werewolves started to become uncommon in the mid- to late 15th century. By this time, the Lycans had gone into hiding and the vampires no longer had any reason to have open dealings with mortals. The humans learned of the immortals again soon after the events of Underworld: Evolution.
Timeline
Early 400s
<PERSON> became immortal. <PERSON> and <PERSON>, the immortal sons of <PERSON>, were born. At some point, <PERSON> started to use his army to clean up after his children and attempt to hide their presence from humans, but his success at this was limited until the mid-1400s.
1202
<PERSON> was captured.
Before 1400
All Lycans (<PERSON> and his progeny) lived in captivity. The werewolves in the wild were raging, uncontrollable beasts, unable to return to human form. Knowledge of werewolves had probably been relatively common among mortals for centuries. The vampires offered protection to the humans in exchange for tribute and slaves.
ca 1400
<PERSON> escaped the vampires’ castle and led the battle against the vampires. The Lycans took over the castle and the surviving vampires fled.
Vampires used livestock for food almost exclusively.
<PERSON> killed <PERSON>’s family and turned <PERSON>.
Early to mid-1400s
<PERSON> faked his own death. The castle was burned, Lycans went into hiding, and the war was seemingly over.
After this point, since the vampires were actively seeking the Lycans and still couldn’t find many, it’s unlikely that mortals saw Lycans frequently, or the humans at least did not know that the Lycans were not human.
It’s hard to say how many pre-Lycan werewolves escaped when the castle burned. 88
Since <PERSON> was still alive, the surviving werewolves probably regrouped with <PERSON>. Since <PERSON> became <PERSON> around this time and had no knowledge of this kind of werewolves until <PERSON> told her about them centuries later, there were probably few or no werewolves in the wild. Since <PERSON> knew nothing of werewolves, first-hand knowledge of them among humans could not have been common.
Since the Lycans and werewolves weren’t a visible threat, the vampires would not need to offer protection to humans. <PERSON> had forbidden feeding on humans, further reducing the possibility for interactions between vampires and humans.
Early 1500s
Any humans who were aware of the Lycans before their castle was burned would have died of old age by now.
Late 1500s
Any humans who personally knew someone who remembered the time before the Lycans’ castle was burned would have died of old age. By this time, knowledge of vampires and werewolves would have been very rare among humans.
Early 2000s
Vampires and werewolves were still unknown among humans. The war between Lycans, vampires, and hybrids escalated. <PERSON> died. Those loyal to him no longer attempted to hide the war from mortals.
Because of <PERSON>’s death and the escalating war, the humans soon learned about the immortals and started their war against them.
As for modern surveillance and regulations, the immortals only remained unobserved for a few decades in modern times. Also, <PERSON> had access to his own technology that he employed to hide their existence. Ultimately, it was only a matter of time before the immortals became known to the humans again.
References
Early 400s
Underworld, an hour and 26 minutes into the film, explanation from <PERSON>, the Lycan scientist:
<PERSON>, Hungarian warlord, who came to power in the early seasons of the fifth century.
Novelization for Underworld: Evolution, page 272:
After sixteen centuries, <PERSON>, the father of all werewolves, was dead.
1202
Year given at the start of Underworld: Evolution.
Before 1400
The events of Underworld: Rise of the Lycans.
ca 1400
<PERSON> was turned around the year 1400, just after <PERSON> escaped.
From the beginning of Underworld: Evolution, narration from <PERSON>:
For six centuries I was a loyal soldier of the vampire clan.
From Underworld: Evolution, 55 minutes into the film (emphasis mine):
<PERSON>: It’s <PERSON>’s prison: the prison your father was commissioned to build.
<PERSON>: What is it? What’s wrong?
<PERSON>: She now understands why her family was killed. 715