No emails are being received for any of the thresholds (4245047)

I have not received any emails for threshold violations.
The only email that has been received is when I press the "statuses calculation" button.

Working as designed.

You will get a notification about servers and database statuses only after executing Statuses Calculation.

WORKAROUND:
If you need an email saying that you have indexes that are Defragmented at either Critical or Warning levels, you should use Analyze Fragmentation.

To configure Analyze Fragmentation do the following:
1. Run Intelligent Defragmentation wizard.
2. On Intelligent Defragmentation settings step check | Analyze Fragmentation and send report. Press Next button.
3. On Select Databases for Automatic Defragmentation and Reporting step check instance or several databases you want to analyze. Press Next button.
4. On Report Schedule Settings step select the notification service to use, enter or select from the address book the email addresses of the recipients to notify, and set schedule for report generation. Press Next button.
Note: Notification services (Database Mail and SQL Server Mail) should be already configured on your repository server.
5. Finish the wizard. As a result qcm_AnalyzeFragmentation_Job will be created on the selected instance. You can run it manually or by schedule.

After the qcm_AnalyzeFragmentation_Job has executed, you will get following report (as an example):

Legend: Instance name (Number of all found indexes,
Number of indexes that exceeded defined thresholds,
Number of indexes that need to be reorganized by reorg command/
Number of indexes that need to be reorganized by defrag command,
Number of reorganized indexes)

Test\SQL2005 (43688,10,10/0,0)