They don't send any emails for test completion. I Logged in (I do this every morning) and noticed the update. The update wasn't there when I logged in yesterday, looks like tracker is updated with a few days delay.
I completed my test last week and tracker updated today (December 19):
Submitted: August 1st
AOR: September 29
BG completed: October 3
Test invitation: December 9
Test done: December 12
Test completed on Tracker: December 17