It seems (am I doing something wrong?) that I cannot find a timezone by simply using the keyboard and incremental searching (that should focus on the part efter the slash). Instead I have to use the mouse to select from a long, long, long drop-down list of possible timezones. For every team member.
All data is stored in the browser locally. This is using local storage as I'm not storing anything too big.
Source: https://github.com/searchableguy/website