This re-wrapping technique seems to defy the laws of healing but I suppose if it's working for people then go for it!
I dont like to wrap my tattoo at all and simply come straight home with an uncovered tattoo. I then gently wash it with warm water and an unscented soap. After that I get some cold water and give the tattoo a quick blast of that to close the pores. (Old Yakuza Trick). I then Leave it to air dry and apply a cream After Inked is the one I use currently. Its important to make sure you don't overdo the cream! I will then wash with the soap and apply the cream/anointment once maybe twice a day for the 1st week. I then start to use an unscented moisturizer to stop it drying out once per day
I always walk around the house naked after a tattoo session I say let the air get to it to help the healing not cover it up :)