The Second Salemers were led by Mary Lou Barebone, who was descended from Scourers, who were aware of the wizarding world.
In the JKR writing on Pottermore about the history of magic in North America focusing on the seventeenth century and beyond, we learn about the Scourers, a group of wizard mercenaries who sold other wizards and Muggles to the Muggles during the Salem Witch Trials, were cast out from wizard society for betraying their kind, and passed on their hatred of the wizarding world to their offspring.
The vengeful Scourers, cast out from their people, passed on to their descendants an absolute conviction that magic was real, and the belief that witches and wizards ought to be exterminated wherever they were found.
- Seventeenth Century and Beyond (Pottermore)
The Pottermore writing on Rappaport's Law refers to a Bartholomew Barebone as a descendant of Scourers, who inherited their belief in and fear of magic.
Unbeknownst to Dorcus, Bartholomew was a Scourer descendant. Nobody in his family was magic, but his belief in magic was profound and unshakeable, as was his conviction that all witches and wizards were evil.
- Rappaport's Law (Pottermore)
There doesn't seem to be any explicit confirmation that Mary Lou Barebone is related to Bartholomew Barebone. However, the entire History of Magic in North America writing was written to promote Fantastic Beasts and Where to Find Them. It seems highly unlikely that two similar characters, with clear parallels to each other, would coincidentally share a last name. Further connecting Bartholomew to Mary Lou, one of his methods was handing out leaflets stoking anti-magic fear.
Bartholomew further printed leaflets giving the addresses where witches and wizards congregated and sent letters to prominent No-Majs, some of whom felt it necessary to investigate whether there were indeed ‘evil occult parties’ happening at the places described.
- Rappaport's Law (Pottermore)
It's unknown if Mary Lou had ever seen magic herself before starting the Second Salemers.
The only time mentioned that Mary Lou was near magic and probably saw it was when Tina was angry at her for beating Credence and mistreating her adopted children, who she neglected in favor of making them work as part of the New Salem Philanthropic Society. This certainly couldn't have been the incident that started her crusade against witchcraft, because she had already begun it, which was the entire reason that Tina had been investigating them to begin with.
“NEWT
(realizing)
And she was the No-Maj you attacked?
TINA
That’s how I lost my job. I went for her in front of a meeting of her crazy followers—they all had to be Obliviated.”
- Fantastic Beasts and Where to Find Them: The Original Screenplay
She cast a spell directly at Mary Lou, so it's very likely that Mary Lou would have been aware that something hit her, and if she saw the spell being cast she probably could figure out it was magic.
“We move into the pool and follow one of Tina’s memories: Tina walks
inside the Second Salem church and up the stairs. She finds Mary Lou,
standing over Credence, belt in hand—Credence looks terrified. In
anger, Tina casts a spell, striking Mary Lou.”
- Fantastic Beasts and Where to Find Them: The Original Screenplay
After the incident with Tina, though, Mary Lou was likely Obliviated. The Aurors had to Obliviate all of her followers that were present at the time Tina used magic. MACUSA would have probably made it a high priority to make sure that she was Obliviated as well, especially with her hatred of magic.