I find you have to RUB it a little with a cloth to get all the rust off, if you just soak it and gently pull it up it won't seem like all the rust is gone, but wipe it down with a terry cloth and you'll see just how clean it is (or if it needs more soak-time). I don't find neutralizing is required nor a clean water rinse-out since the slightly acidic solution when dried inside the tubes doesn't seem to cause harm: worst case is that if moisture invades the interior it might just re-activate the tiny residue of OA and that wouldn't be so bad....but YRMV.
I always use some kind of waxy-oil to coat the inside of ALL steel frames: cheapest is BLO, most costly is FrameSaver but I have also used WaxyOyl (only in UK, I think) Boeshield and LPS #3 ...which all work well, too. I think WD40 is a waste of time/money for this purpose, but it's probably as cheap or cheaper than BLO.