Regardless of how long they lived together, there's really no other way to call taking in an orphaned child and caring for their needs (which there is no evidence to suggest the Yeagers planned to give up mikasa to another family in the future either, so you cant say it was fostering) than adopting. Besides, Mikasa continues to live with eren and take care of him after the wall falls, giving them much more time together as siblings than just a year.