Yeah, It properly working. But for time tracking you will have to download the upwork time tracking app. Which will be installed in the system itself. It will be also activated automatically when you start or click on the start button of the client work.
There is no official word from Upwork on whether or not their timetracker works on Chromebooks yet. However, there are some users who have reported that it does work on Chromebooks. If you are using a Chromebook, you may want to try it out and see if it works for you.