This was answered here: How to fix cesium timezone？. You can override the timeFormatter or dateFormatter functions which take a date/time and return a string that appears in the clock widget.
To handle displaying the timezone correctly you’ll probably want to use another library to take care of that formatting. Here is a JSFiddle that uses the Luxon library to set the time to the user’s local timezone, and you can use this to set the time to a specific timezone as well: