Since the beginning of the year I have received 3 packages sent via different carriers with tracking information. All three had been delivered before I got an email saying they would be delivered the next day or the day afterwards:)
Even RM, where they usually send the delivery email saying delivery today but often actually deliver a few days later, delivered it two days before the "delivery today" email was received. In this case the "24" package took less than 24 hours in their system.
Emails were not delayed as the headers indicated that they were sent very shortly before being received.
Luckily all the packages were letter box size so no problem second guessing when they would be delivered.