People moving from Puerto Rico to the US aren't living in a different country. They’ll continue to pay taxes to the same country (in fact, more taxes to the country), but they won't pay local taxes in Puerto Rico, for the same reason a US citizen who used to live in San Francisco but now lives in Salt Lake City doesn't pay taxes in San Francisco or California.

Puerto Rico is a US colony (or, more politely, territory), not a foreign country.