I looked it up:

Tattoo needles are more like the nib of a fountain pen than a syringe; the ink isn’t shot down through the needle, but suspended at the end of it when an artist dips the tool into a well. Then, when the tip of the needle pierces a hole in the recipient’s skin (both the epidermis and the dermis beneath it), capillary action—the same force that makes liquid creep up the sides of a straw—draws the ink down into the dermis.

Source: https://www.popsci.com/how-tattoos-work/

IKR? But yeah, nah, tattoo machines are basically a motor that pumps the needle up and down, and you have to dip it in ink to transfer it into the skin.