The United States would be concerned about recessions in these areas because these are important trading partners for the US. In today’s globalized economy, the health of one economy can impact another. If recessions arise in markets that import a great deal from the United States, the US economy could be harmed. The recessions would cause demand in those countries for US imports to fall. As the US lost its ability to export to those countries, aggregate demand in the US would fall. This could cause GDP to fall, putting the US (possibly) into a recession as well.
Therefore, countries have to worry whenever major markets for their exports go into recession.