On some ancient ones, it says they have non-human worshippers (Leng Spiders for Atlach, etc.).

Question: would these worshippers then fall under the definition of "cultists" for that game? Like would the Tulzscha herald make said Leng Spiders elusive and undo seals?

Question 2: Do regular cultist monsters no longer fall under the definition of "cultists" in these cases (ex. Cultist monsters with Atlach and Tulzscha don't become elusive, only Leng Spiders)?

1 and 2) Such monsters are not "Cultists." Only Cultists are cultists, and so are Children of the Goat and the Dark Druid (because their pieces says they function as Cultists). When rules like Tulzscha's first gate or certain encounters say to take a Cultist from the cup, I usually make sure it's an ordinary Cultist in those cases (as opposed to a Child of the Goat or a Dark Druid).

There's room here for a house rule though!