So before they could really "adopt him", it really all depend if neither of his parents really wanted to take him in. After scheming and getting his dad sent to jail was all done and over with, the only thing left was to see if his mother would ever come back to claim him. So technically, because she did come back and wanted him back, I believe they were unable to legally adopt him. Regardless, he never spent a dime of their (his biological mother's/new husband's) money or asked for help in anything, so even though legally he wasn't able to get adopted by MC's family, he viewed MC's family as his true family (adoption papers ain't gonna stop him). After he ran away the first time to MC's home, he did ended up going back to his biological mother's home but only because he didn't want to trouble MC's family with his situation. Regardless, he still kept contact with them.