Do they use UPS?
I worked in shipping using UPS for 15 years, this is what happens...
When your order is actually boxed up, it goes on a UPS scale, your name and address already loaded into computer, the shipper clicks the "ship" button, zebra printer spits out your label... In UPS's program it has shipped.
But your box-o'-stuff may not actually leave MS until the skid/truck/trailer is full!
That could take 1 or 2 days.
Only next-day-air shipments left that day, usually within a hour.
So when you track a package, it says it shipped (according to their program) but it's still waiting to be literally loaded on to the truck.