Merlin in Geoffrey of Monmouth's History of the Kings of Britain (1135) is more or less a combination of two possibly real persons, 5th century King Aurelius Ambrosius in the Historia Brittonum (or of the part where Aurelius Ambrosius is a magical boy confronting Vortigern) and Mryddin, a legendary insane seer from late 6th century Britain, plus maybe a few other possibly real persons, and a lot of imagination. And the Merlin in History of the Kings of Britain is the basis for all the Merlins in all the medieval romances.
So the possibly historic Merlins would be two (possibly more) men living during the period of AD 400 to 600, about 1,418 to 1,618 years ago. Though a magical wizard version of Merlin could have been many centuries old when he was active in post Roman Britain.
Nimue is a much more fictional character, first appearing in medieval romances set in the time of King Arthur, who flourished roughly 516 to 537/8/9, or who maybe died in 542, according to various dubious sources. Every medieval person interested in the date of King Arthur's reign could easily find out that he was supposed to have lived in the 6th century and possibly also in the 5th century.
So no medieval writer would have any reason to have Nimue meet and later enchant Merlin at the court of King Arthur in any era other than the 5th or the 6th century.
Nimue is a fictional character living in the 6th century according to medieval stories. Putting Nimue in any other era is like having Julius Caesar meet Napoleon, or Genghis Khan meet U.S. Grant.
So I strongly suggest that the "200 years ago" may be a clumsy way of saying "200 years earlier" than an event many centuries before the present day, 2018. If there is no way to make the "200 years ago" refer to a suitably distant era maybe the writers meant "2,000 years ago" and someone left out a zero. Or maybe the writer of that episode has no idea of chronology.
I point out that according to the OP Merlin gained immortality and magic by drinking from the Holy Grail 1,000 years before the age of Arthur (which was 1,500 years ago) and thus 2,500 years before the present year 2018. The holy Grail is usually supposed to be cup that Jesus drank from at the Last Supper, and/or that was used to collect his blood at the Crucifixion, both events happening about AD 30. So what made the Holy Grail so holy and magical back around 500 BC, centuries before the time of Jesus? Is that an anachronism?
Did the creators of Once Upon a Time decide to disconnect the possibly originally pagan Holy Grail from Christianity, or did someone simply forget to do any "time computation"?
So it is possible that there is no way to make the various chronological details in Merlin's biography in Once Upon a Time consistent because the writers were too careless. I hope that is not the case.
added 10-10-2018 According to the OP The ABC Hulu site mentions a man named Vortigan "200 years ago". Vortigan sounds a lot like Vortigern, which is a version of the name of the real or imaginary British King who hired Saxon mercenaries to defend Britain. According to Bede writing about 730, the Adventus Saxonum, or first coming of the Saxons, was in 449 AD, while the writer of the Historia Brittonum writing about 830 AD said the reign of Vortigern began at a date calculated to be about 425 and the Adventus Saxonum was in 428 AD, while the Anglo-Saxon Chronicle written about 880 mentions Vortigern in the years 449 and 455 AD.