The artist should be using these tiny little cups called "ink caps" to put just enough ink in for your tattoo, and whatever is left should be thrown away. The same goes for the water and ointments.
This brings to mind another point: Many artists will use deodorant to create a darker impression of the transfer copy on your skin before they begin tattooing. This is a very effective method, but the artist should never use the deodorant stick directly on your skin. It has been used by other clients. Instead, the deodorant should be wiped onto a tissue, and the tissue placed on your skin.
You should never have direct contact with the deodorant stick. If they touch you with the stick, who knows how many others they have also touched with it.
