I have had this happen in other types of bar charts, where the data labels show up in Tableau Desktop but not in Tableau Server. With my charts, this was a spacing issue. When I increased the height of the bars by just a couple pixels, the labels started showing up when I published them.
If you can post your workbook I will just see how to tackle this.
I have sample local host set up in my machine and I can remove your workbook after I found the solution for you
Please attach your workbook if you are fine.