When does the term 'african american' no longer apply?

Here in America the term 'African American' is used as a nice way to say black. I understand how this applies to those who were once native to Africa. When specifying one's previous nationality I understand it is common to place it before the word American. For those individuals who have parents of that nationality they are referred to as second generation (insert nationality) American. For example, a German couple becomes citizens on the U.S. They are than German American. Their children would be 2nd generation German American. For how many generations are they still referred to as German American. 2nd? 3rd? Or so on? I ask this because the term African American is used for all black people without specification of the generation. I know several people who find this offensive because they are not African but Jamaican or from another country. Is it wrong to use the term African American to apply to all these people? And at what point does the term no longer apply as in they can no longer count the generations? When is a person simply American?