When upgrading the primary, if there is no manual intervention required on the workers, then under worker program/features, it will show the old version.
If you want to verify, you should be able to navigate to the bin directory on the primary and worker and verify that it's the up-to-date version this way. Here's a screenprint of what it looks like on my worker for the 10.5.3
Jeff has a good way to find out the version of the workers and we've had a number of support cases where folks aren't quite sure if the workers themselves upgraded or not. This is going back from memory but with more recent versions of Tableau Server the Primary queries the workers to see what version they're running. If there's a mismatch, Tableau Server will fail to start.
We do have a KB article that provides more background on when it's necessary to do a manual install of worker software versus when the Primary can "push" the upgrade packages down to the worker:
In older days there wasn't any option and you always had to manually upgrade the workers. Whereas Tableau's development team tried to make multi-node upgrades easier but as the article mentions once we update the version of Postgres a manual upgrade will be necessary but the installation program run on the Primary should give a heads up. It's always best to try an upgrade in a non-Production environment first and these don't have to exactly mimic Production but hopefully will have at least one worker if your Production system is multi-node.
Mark. Thanks for the link to the KB article. I knew there was one out there...
I tried running the above command and I see the new version name but with error message like below
log4j: ERROR Failed to rename [D:Tableau Server/logs/tabsvc-tabadmin-java.log] to [D:Tableau Server/logs/tabsvc-tabadmin-java.log.2018-07-12].
Can I ignore the error message or do I need to take any action on worker nodes?
This is going from memory which isn't what it used to be. More than likely the tabadmin command will really only work on the Primary versus the Workers. One other method I forgot was that just like the Primary, each Worker has its own tabadmin.log file. The tabadmin.log records what happens when you first start up Tableau Server in addition to the outcome of any "tabadmin commands" that you run. In that file it should reveal the version along with resources such as memory, CPU. Basically that gets logged everytime Tableau Server starts up. The only trick there is these files can retain a lot of history so you want to start from the bottom of the file and search up. If you start at the top of the file you'll most likely see the older versions that they were on at one time.