When taping with automatic taping tools, is there a specific order I should follow?

While everyone has their own preference in the order that they tape a room, most automatic tool users will tape all the drywall butt joints (where two non-tapered edges of drywall meet) on the walls and ceilings first as they move around the job. These butt joints are wiped down with a taping knife and pan to press the tape into the joint compound and remove the excess mud. 

After the butt joints are taped and wiped down, all the flat joints (where two tapered edges of drywall meet) on the walls and ceilings are taped. Like the butt joints, the flat joints are wiped down with a taping knife and pan to press the tape into the joint compound and remove the excess mud. 

The final step is to tape the internal corners with the Automatic Taper, immediately followed by using the Corner Roller and Corner Finisher to produce a machine finished corner that is already embedded on both sides.