I would imagine that the colonists and immigrants would have brought their folklore and mythology with them, but it appears not to be the case.
Is there an explanation for that?
While more can always be said, /u/itsallfolklore has answered a similar question here.
Thanks to /u/thefourthmaninaboat for the link to an answer I wrote in the /r/AskHistorians Bronze Age (i.e. long ago).
If you have additional questions after reading that answer, please let me know.
The simple answer there is that people always pack their folklore and carry it with them when they travel - it is inescapable - but their traditions do not necessarily thrive in new places and beliefs and stories rarely diffuse in the new environment. And yet, ... sometimes they do (and did!).
Someone more qualified than I should be able to expand on this, but what about tommyknockers?
They're fairy-folk that live in mines and warned miners when shafts would collapse, or else caused cave-ins themselves. A direct result of Cornish miners bringing folklore across the pond (the Cornish called them "knockers", I'm not sure why "tommy" was placed in front of it in the US, but I suspect it's because the US already has a definition of their own for "knockers")