My routine is pretty much always the same: Neck arrives unstrung. I remove t-rod adjusting nut (if it's the kind that comes off), use a pipe-cleaner to clean the threads, apply some graphite grease into the adjuster nut's threads and on the bearing face of the nut, put nut back on and tighten it all the way (oh crap, sometimes it needs spacers added). String the sucker up and check relief. If it's dead straight or just slightly back-bowed, then in the "set-up" jig it stays for at least a day. If I see right away there's extreme back-bow or extreme relief, I don't want to leave it that way and will adjust to something more reasonable (but at *this point* favor slight back-bow over any relief). If the relief is extreme (which I see all too often these days) then I have to get all medieval chiropractor on it's ass, and then into the set-up jig to settle. For pre-fretwork I want it as dead straight as possible. For a "ready to gig" set-up, I would rather have .002" to .005" relief than even a hint of back-bow.
The main thing is, often you have a neck adjusted straight, and within 24 hours it'll creep into more relief than you wanted.
I don't think there's any reason why the guitar would need to be "face down" when helping the neck adjust.