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Publishing a workbook is one-time thing. If you make changes offline in Tableau Desktop, those changes will not be reflected until published again. Tableau Server/Online is the sharing tool where you put the Workbooks once you're done designing them in Tableau Desktop. (this is a very simplified explanation). If you have made changes to a workbook in Tableau Desktop and you want those changes reflected in Tableau Online, republish the workbooks, overwriting the old workbook. This video on the process might help you out: Publishing to Tableau Online | Tableau Software
Does that clear things up?
Yes, thanks for stating it so clearly!