I always rinse my bottles out after pouring so I never have to "clean" them afterward.
When I get ready to bottle I just use the bottle washer - the red one with the pump and reservoir - give it 5-6 pumps, remove the bottle from the shaft and place the neck into the solution for a second or two, remove, re-pump more solution into the bottles to remove any bubbles, then place them on the drying rack. Nothing more, nothing less.
Using iodophor says 2 mins contact. Even with the bottles draining they are "in contact" with the solution for at least 2 mins. Sometimes even after an hour on the rack there is still some solution in your bottles?