Why doesn't the burndown chart change when I change the tracked time?

This is because the burndown chart is based on the values in the "Remaining" field in the backlog items and tasks. The burndown shows how much work remains, not how much time has been used.

Also, it's the dates where you change the "Remaining" field that matter in the burndown. So, the dates of the used time entries don't matter for the burndown.