I did a Google search today with my family name, and was surprised to notice that there are so many of us. I belong to the Carelian (Eastern Finland - Western Russia) branch of Tattis.
Seriously speaking I don't think there is any genealogical link with our family and the Italian Tattis, though it could be that some descendants of the Carelian Tattis also live in America.
The common name 'tatti' in Finnish means a type of mushroom (boletus). In ancient times it was customary to choose family names from names of animals or plants that were supposed to have magical properties.