Given the nature of the transformation, this is clearly magical. As Kate said, you get to decide how the magic affects tattoos.
What would be the most interesting for your story?
If the story takes place in the otherwise real world, tattoos on a child would certainly draw attention, and perhaps lead to all sorts of delicious conflict (what sort of lowlife artist would tattoo a child, what sort of parent would allow that, etc.). And the attention and conflict might be greatly amplified by the nature and location of the tattoos.
Do you want that sort of attention and conflict in your story? If so, make the tattoos survive the transformation.
What might make the loss of the tattoos interesting? What is the story behind each tattoo? What meaning does each tattoo have for the character? How strongly does the character identify with each tattoo ("this is part of who I am")?
Would the loss of the tattoos be troubling for the character? Do you want that kind of trouble in your story? If so, lose the tattoos.
Tattoos are useful for identification. Do you want to make it easier or harder for the character to convince people who he really is? Do you want to make it easier or harder for the character to hide his true identity?
Finally: Perhaps the tattoos could be transformed in some interesting way. Maybe they shrink, or stay grownup size, or change form or color, or have an aura, or only certain people can see them, or they itch or burn as if they don't belong, or they confer some magical ability (which perhaps consumes the tattoos), or...