Tableau Public doesn't work like Server or Online. You can only pass up Workbooks that have the Data contained within it (Aka Extract). You can tell if it is a packaged workbook by the file extension .twbx
Here is how to effectively publish to Tableau Public
Also, you will have to manually update the Extract with new data, and then re-publish to Public. There is no workaround for that. (Maybe with a custom PowerShell script and TABCMD, but I am not 100% on that).