Does an author have to submit an article to Math databases once it has been published in a journal?
For Zentralblatt or MathSciNet, which are by far the most important databases in mathematics, there's no need to manually submit anything.  I would assume the same is true for any comprehensive database (if you depend on author submissions, you won't get anywhere near complete coverage), but I suppose it could depend on the particular case.  I've never heard of ResearchBib, so I can't say anything there.