Yes … SSA is the program where Amazon uses data from your shipments to set the customer’s estimated delivery date on the order.
We ship only via USPS and have SSA enabled. Generally for us, the given transit time has been 1 day longer than the actual delivery time by USPS … so we have had no problems and 100% OTDR. We would note that we also have AHT enabled and follow a strict 2 day handle time. With these programs, consistency is the name of the game for them to work without any hiccups.
If you set up your SSA template to have only standard shipping option with only one preferred shipping service, you will not have this issue. If you try to offer economy, expedited, 2 day, 1 day and/or same day, then yes you could run into this issue.