In principle the GA boarding the flight from the USA to the schengen country is responsible for checking documents, but with a valid USA passport and a boarding pass that's printed as "DOCS OK" (which implies that the "DOCS OK" authorization has been entered into the DL system), in practice the GA isn't going to check further.

However, the son should be ready to at least be able to show the email stating the plans to be in Croatia. He should keep hotel receipts for all nights out of the schengen zone and make sure to get his passport stamped at the border in both directions.