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.
Alexander Corvinus became immortal. William and Marcus, the immortal sons of Alexander Corvinus, were born. At some point, Alexander 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.
William was captured.
All Lycans (Lucian 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.
Lucian 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.
Viktor killed Selene’s family and turned Selene.
Early to mid-1400s
Lucian 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. Since Lucian was still alive, the surviving werewolves probably regrouped with Lucian. Since Selene became a Death Dealer around this time and had no knowledge of this kind of werewolves until Tanis told her about them centuries later, there were probably few or no werewolves in the wild. Since a Death Dealer 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. Viktor had forbidden feeding on humans, further reducing the possibility for interactions between vampires and humans.
Any humans who were aware of the Lycans before their castle was burned would have died of old age by now.
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.
Vampires and werewolves were still unknown among humans. The war between Lycans, vampires, and hybrids escalated. Alexander Corvinus died. Those loyal to him no longer attempted to hide the war from mortals.
Because of Alexander’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, Alexander Corvinus 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.
Underworld, an hour and 26 minutes into the film, explanation from Singe, the Lycan scientist:
Alexander Corvinus, Hungarian warlord, who came to power in the early seasons of the fifth century.
Novelization for Underworld: Evolution, page 272:
After sixteen centuries, William, the father of all werewolves, was dead.
Year given at the start of Underworld: Evolution.
The events of Underworld: Rise of the Lycans.
Selene was turned around the year 1400, just after Lucian escaped.
From the beginning of Underworld: Evolution, narration from Selene:
For six centuries I was a loyal soldier of the vampire clan.
From Underworld: Evolution, 55 minutes into the film (emphasis mine):
TANIS: It’s William’s prison: the prison your father was commissioned to build.
MICHAEL: What is it? What’s wrong?
TANIS: She now understands why her family was killed.
SELENE: But that was many years later.
TANIS: The winter of Lucian’s escape. Your father knew too much.
Underworld, an hour and 53 minutes into the film, statement from Kraven:
But let me tell you something about your beloved dark father. He’s the one who killed your family, not the Lycans. Never could follow his own rules. Said he couldn’t abide the taste of livestock, so every once in a while he went out and gorged himself on human blood.
Early to mid-1400s
The beginning of Underworld, narration from Selene (emphasis mine):
The war had all but ground to a halt in the blink of an eye. Lucian ... had finally been killed. The Lycan hordes scattered to the wind in a single evening of flame and retribution. Victory, it seemed, was in our grasp. ... Nearly six centuries had passed since that night, yet the ancient blood-feud proved unwilling to follow Lucian to the grave.
At the time, Selene didn’t know that Lucian had actually survived, but she was probably correct about the year, since she was already a vampire by this time. She apparently didn’t raid the castle, perhaps because she was not yet a full-fledged Death Dealer.
Events from Underworld and Underworld: Evolution.
From the beginning of Underworld: Awakening, narration by Selene (emphasis mine):
Then I found Michael Corvin... and everything changed. ... We retaliated, killed the elders. And for a brief moment of time, we were safe. But then, a new darkness arose.
The film proceeds to depict the war of humans against the immortals. The Underworld Wiki says that this film was set six months after Underworld: Evolution, but I don’t know their source for that claim.