Imagine a magazine that has not published you before does so.
When this happens, follow up promptly, and that means being ready to follow up promptly. Once a first article is published (not accepted – publication could be cancelled or delayed) get in touch with the editor again. Thank them, invoice them if necessary (though I think this is best kept separate as such a note will be passed quickly to the accounts department). A little flattery may be good, saying it is good to see your work in such a journal or that the way it is laid out is pleasing. If you have received reader comments that may give you something worth mentioning.