Find your tribe in a Sea of Creativity
Vincent feel into a deep depression during the months following William invoking him, causing Vincent to frequently forget to fulfill his basic needs like bathing and eating. So, William would do it for him. William would fill up his bathtub and carry Vincent from his bed to the bathroom and bath him, he'd bring a blood bag or two to Vincent's room and sit him up and help him drink it while rubbing his back, he'd sit Vincent in front of himself and brush out his matted hair carfully so he wouldn't pull Vincent's hair.
The reason William sees Vincent as his child is because he had to take care of him in the way you would a small child - helping bath them, brushing their hair, feeding them, ect. William wants to care for and protect Vincent because once he started he couldn't stop.