A USPS package arriving late can be caused by it not getting onto a truck or plane before it goes off to the destination.
For example your package may have arrived at the USPS sorting facility later than normal and didn't get onto the destination truck or plane in time before they left with other packages.
Or the truck or plane got too full of packages and they couldn't fit your package on that truck or plane.
Also sometimes I've had my USPS tracking say in transit and arriving late the night before and the next morning I checked my USPS tracking information and it said it arrived at my local post office and was out for delivery.
So sometimes the USPS tracking will say In Transit Arriving Late but still the package may arrive on time.
But if it's late then it will usually only be one day late if it's on a weekday.