Base provides just the one master time zone for your entire account. This time zone can be set by following this guide, and will apply to all the users on your account.
All calls, data creation, and editing timestamps will be recorded based on this time zone. That said, Appointments and Tasks will be displayed on a users calendar based on their computer's time zone setting.
We're exploring adding multiple time zones to Base in a future update - if you'd like to see this added, share your feedback here on our UserVoice page!