I'm afraid that I don't recall the name of the manufacturer, but there is a company that makes a box & support that can actually be installed through the 4" hole in the ceiling without making any trips into the attic.

Otherwise, try this, rip or plane a 2x2 to a thickness of 1" (when dealing with 1/2" drywall). Lay 2 pieces of this 1" thick material on the top of the drywall on either side of the hole in the ceiling. Lay a 2x4 flat on the 1" spacers. Run 3" long drywall screws through the joists or trusses to secure the 2x4 in place. Poke wire through the hole, go downstairs & install the wire into the box, push box through the hole & secure to the 2x4. Hang fan. Crack open a cold, you've earned it.

Tom

Few things are harder to put up with than the annoyance of a good example.