Why do tasks with anchor date “start date” not trigger on start date?

This might happen if, under the “Applies to” section of the task list settings, the “Hired” lifecycle status is only selected..

This means that on the start date, the new hire is moved to “Employed” lifecycle status, therefore no tasks will be triggered from this point since they no longer are included in the applies to section.

It might be a scenario where:
A. Task list owner has permissions to “Employed” employees only;
B. Tasks are sent at 00:00 (task list owner time zone)
An employee changes their lifecycle status at 00:05, so at 00:00 the employee is still in “Hired” status.  At this time, the task list owner does not have permissions and the tasks fail to be sent.