The Halacha was prior to World War 2 if you moved to a community you became part of that community and followed their customs. So if someone was born in Vilna and moved to Baghdad (and stayed) , they became an Iraqi jew even though they were born in Vilna.
After World War 2 , everything became mixed up and this no longer appled. However Rav Yosef was born in Baghdad prior to the emigration of most jews from Iraq so he was Iraqi even if his ancestors came from Spain