Everyones skin's different so it might not be the tattooer. Here's what I do. Since my shop is a hour away. I drive home with the wrap still on, fill the skin/tub full of really warm/hot water. Then I wash the my arm in seperate water then submerge the tattooed area in it for about 10 minutes. From there i'll use a non-abrasive soap the further clean it.
My shop gives out small packets of a stuff called Fougera. Which to the best of my knowledge is very similar to aquaphor. It's a simple ointment that contains Bacitracin Zinc and some petroleum products. It's always helped all my tattoos to heal exceptionally well.
When I no longer have that, I go to Aquaphor and any other Bacitracin Zinc based product. I keep it moist, but not clogged and my arm heals almost fully in under a week.