If they do not accept reprints, that means they are seeking first publication rights -- they're only looking to buy a story if they can be the first to publish it.
The thing is, any sufficiently public place you've posted your story, counts as publication. It doesn't matter how many readers your story has actually reached, only whether a reasonable reader could have read your story by buying a particular product or going to a particular website.
- Posting your story on your blog counts as publication.
- Posting your story on Wattpad counts as publication.
- Self-publishing on Amazon for three days and then taking it down, counts as publication.
- Emailing a friend your story doesn't count as publication.
- Writing a blog post saying "I've written a story; friends can contact me privately for a copy" doesn't count as publication.
- Sharing your story in a private, password-protected writers group doesn't count as publication.
- Selling your story to magazine, but then that magazine collapses and never puts out the issue with your story in it, and eventually it returns your rights to you -- doesn't count as publication.
A good rule of thumb is: If people could ever buy your story (in some format) then it is published; if Googling a phrase from the story turns up the complete story (or has in the past) then it is published; otherwise it isn't published :P
As for being able to self-publish later, it depends entirely on your contract. Some contracts might require various rights to reprint, archive, or anthologize your story, or various forms and lengths of publishing exclusivity. (For example, if I'm publishing a magazine on May 1st, it would be silly of me to allow authors to self-publish on Amazon on May 2nd, possible with a shiny banner reading AS PUBLISHED IN STANDBACK MAGAZINE :P ).