There are a couple of reasons that your tracking number might reflect a "Delivered" status, even though you just generated a label or shipped the package.
Incorrect scan event by USPS:
If your packages show as "Delivered" to the same City and Zip Code as you mailed it from, chances are the incorrect status is due to an honest error.
Post Office employees are people, too, and sometimes they make mistakes. If a clerk has their scanner set to "Delivered" instead of "Accepted", then your tracking will show the "Delivered" status. While this can raise concerns for you and your customers, it should not have any impact on the package's delivery.
Unfortunately, subsequent scans will most likely not update USPS.com's tracking data. However, a USPS customer service representative should be able to provide you with updates via their internal tracking database. Learn more about your options to get tracking updates from USPS.
Recycled tracking numbers:
If your package shows as "Delivered" to the wrong destination, as well as "Archived", odds are that your package received a recycled tracking number.
Occasionally, due to the high volume of USPS shipments, USPS tracking numbers get recycled. However, once the shipping label is scanned, the "new" tracking information for your package will appear.