If it comes up tell them exactly as you told me, "It was not deemed as a demotion." No one is perfect and we all get nervous and forget small details.
Don't sweat it, I feel like you are working yourself up over nothing. I still think that you will be fine, just if they ask be as honest as possible. Keep me updated! Good luck!

Really, it depends on the Institution, but I would imagine if they are currently hiring, within a few weeks...don't quote me on this because every Instution is different!! They will usually ask you how much of a notice you need to give and then they will start you on the next pay period after the notice is up...good luck and please feel free to ask questions, if I can't help you I will get you to someone who can!! Enjoy the site!!!!