If the sites did this, then it would make checkers rather useless, i.e., submitted original work could only be validated once and only once by the submitting author and thereafter would be flagged, as plagiarized. Thus, everything would be flagged as plagiarized by all third parties who use the site to verify anything given to them after the author has checked his work himself.
Plagiarism sites track actual publicly written/available (for example on internet sites and bogs etc.- this is why one should not place essays publicly on CC) and printed material that have been digitized. Since your work has not been and is not publicly available it should not be flagged if checked by a professor or anyone else.
As for reliability, well, understand that the term “garbage in, garbage out” means something. Unless you know what the checkers are checking, then there is zero way to assess reliability.