How does the email notification logic work?

The Timesheet Builder app uses standard Jira notification scheme. With the Timesheet Builder app the logic of nofitications can be customized. The Timesheet Builder logic includes team permissions checks, so if a notification scheme contains All Watchers, as the recipients, emails will be sent only to watchers, who have view worklogs permissions in the team chosen during worklog creation.

Are notifications sent to worklog author if work log was created, updated or deleted by someone else?

Notifications are sent ony to users, who are in the list of notification recipients. By the default worklog author does not get notifications, if a worklog was created, updated or deleted on behalf of this user.

If you want to customize it, you can modify current notification scheme by adding “Assigned worklog author” as recipient. “Assigned worklog author” should be added to the following evets: Work Logged on Issue, Issue Worklog Updated, Issue Worklog Deleted. In this case notifications will be sent to the users, if worklogs were created, updated or deleted on behalf of them.

Is it possible to turn off the notifications about worklog update, creation or deletion?

Yes, you can delete all recipients from Work Logged on Issue, Issue Worklog Updated, Issue Worklog Deleted events.