I checked it also, yeah, using Joomla update does not work properly. You can use JA Extension Manager, it's free. It's the best tool for upgrading JA products. After installing to your Joomla system, go to Components >> JA Extension Manager, in the Services Manager tab, select JoomlArt as your default service. Next, find T3 system plugin, check for new version the hit the Upgrade.
The advantages of the component is that, it has back-up file for each time you upgrade so you can restore if you want. You can also check for new files or changes of files, etc.
Here is the video tutorial:
https://www.youtube.com/watch?v=t6W0bM0duS4
Gardner.