Yes, exactly, hence “per all time, that are still alive” because it’s measuring the current number of American-born residents of each country, compared to the residents from said country in America.
As of what year?
Edit: id also like to point out there are diaspora maps for time frames, so just posting a map with that word is as best trying to misleading or make a statement. Otherwise, that information would be freely available. That’s how data works.
That’s an entirely different thing than “per unit of time”. It’s a valid question, turns out there isn’t an answer, but some very basic searching linked me to the original map as released: http://cf.datawrapper.de/dduui/2/
To your edit, sure, there are diaspora maps for timeframes. Those are called immigration/emigration maps, because the acts of which grow or shrink a diaspora.