Actually you can start time tracking by clicking on that On/Off button that is displayed. Also you can start time tracking by right clicking on upwork tracker in lower right corner of your screen if you are on Windows. But ye I agree that it would be nice if some provides you with solution how to fix this 🙂 .
Could you please let us know which operation system you are using? Also, make sure that another version of Upwork Team App isn't currently installed on your computer.
The available versions of the Team App (including the beta version) can be downloaded here.