Initially, Timetag creates a dedicated calendar for you (named TT - <your organization>), but you can configure Timetag to use a different (Google) calendar, e.g. your default calendar.
1. Click on your organization from the side bar.
2. Click on Calendar Settings.
3. In the Connected calendar box, select the calendar you would like to use.
Check the article Difference between singular and multi-use calendars for an explanation of the Calendar Type setting.
4. Click Update Calendar in order to save your chosen setting.