There are currently four Dreamlifters in existence and they all belong to Boeing. They are operated for us by Atlas Air, the largest provider of contract cargo lift in the world. Perhaps what you saw is the small writing on the side of the plane below the forward edge of the "hump" that says "Operated by Atlas Air Inc." Wikipedia has a pretty good writeup about the Dreamlifter program at
http://en.wikipedia.org/wiki/Boeing_747_Large_Cargo_Freighter[
I suspect they sometimes call at Miami because Atlas has a main base there. So they may stop there for crew changes, routine maintenance, etc. The cities served by the Dreamlifters are Nagoya, Japan (fuselage sections and wings) Grottaglie, Italy (fuselage sections and empennage surfaces) Wichita, Kansas (fuselage nose section) Charleston, South Carolina (fuselage sections), and Everett, Washington.
South Carolina not only winds the two aft fuselage sections but they join all the fuselage sections (except the nose) together into two main sections and stuff them (floors, doors, all the insulation, wiring, ducting, etc). These main sections are then flown to Everett for final assembly or are wheeled across the road into Charleston's new assembly building. The first 787 to be completely assembled in Charleston will be rolled out of the factory at the end of this month.
Charleston is the only plant that does it all--- makes 787 fuselage sections from scratch all the way up through assembling and delivering complete airplanes. "From freezer to flight" is the term I learned last week down there. The only significant 787 components made in Everett are interiors (Charleston recently opened their own new interior shop). So Everett is an assembly plant only for the 787.
The same is true for the 747-8, 767, and 777. The only major components for these planes manufactured from scratch in Washington State are the wings and some empennage surfaces. The fuselage components for all three models are made elsewhere, primarily Japan. They come to Everett by ship and rail as does the entire, assembled fuselage for the 737 which comes to Renton from Wichita courtesy of the BNSF railroad. The 787 is the first Boeing program to employ air transportation of the main airframe components.
Interesting factoid-- all 787 fuselage sections and wings are painted white as soon as they are made. This is because if the raw composite surface is exposed to UV light it almost immediately develops a surface oxide that paint will not stick to. It's a big job to clean this oxide off prior to painting the plane for the customer, so when the program was new all exterior body and airframe moves were made at night and the fuselage sections were wrapped in black plastic for transport to the assembly plants.
This quickly proved to be an expensive logistics nightmare so someone came up with the notion of painting the components white as soon as they are manufactured. So the planes on the lines look like the photo below of an Air India 787 in Charleston (the rudders are painted in the customer livery prior to final assembly because they have to be balanced before they are installed).