Resolution 1: In O365, Task Reminders are sent after the task is overdue. This is determined by the Due Date field in the task settings.
Once the task is overdue, the reminder emails will start to process. If you want to escalate or auto complete the task after all reminders have been sent out, you can set this in the 'Escalate and auto-complete options'.
If these options aren't set the Task will be patiently waiting to be updated.
This information is also listed in the Help Documentation for the Assign a Task action.
Resolution 2: When the Wait for task completion checkbox is not selected, the action will not send escalation or reminder emails.