This is false. AfroAmericans are more likely to put their race (black) before their ethnical name (Afro/African American) or nationality (American). Foreign "blacks" are more likely to put their rooted place of origin (nationality) or tribe (ethnicity) before their race.
Where are you getting your info from breh? Your next door neighbour? What you're say is patently untrue.
Get some stamps in your passport and go travel the world. I've lived in or travelled to the majority of Caribbean islands and every black person refers to themselves as black. Ain't never met anyone who goes around saying they are "Afro-Jamaican", "Afro-Antiguan", or "Afro-Bajan". All say "I am a black man".