Let me add, hold the needle pointing UP and the carb UP, when you insert it in the bottom of the hole. No point fighting gravity.Are you 100% certain that the old washer & o-ring are extracted from the tower. If not then new assembly will not turn-in to fully closed position (coil-bound spring). I've built a tiny little 'fish-hook' out of a piece of mechanics wire to reach inside the towers.
I would has said that in reverse. starting with the needle. I put a little oil on the shank of the needle & its threads. Then install the spring on the needle, then the washer, then the o-ring. Install the Assembly into the tower.