US built freight cars for export to Cuba met then current AAR and ICC requirements. They were sent over US railroads in regular freight trains to port(s) where they were put aboard ships for Havana. Export passenger cars for Cuba, due to their length, likely went as deck loads on freighters.
Besides West India Fruit and Steamship, SeaTrain Lines was another outfit. It had a route to Havana from New York and I think out of Charleston SC as well. I'm not sure about New Orleans but it could be possible.
At the time US cars were going to Cuba with shipments, they usually came back with export loads to the US - until the Battista regime was overthrown by Fidel Castro. It could be that some US railroad equipment got stranded there from that revolution.
The matter of Cuban railways rolling stock not meeting US standards may have primarily concerned inadequate maintenance and repair. Otherwise, Cuba's main railways had the same standard gauge, Westinghouse air brake and AAR couplers that US railroads used.
The US exported a good deal of railroad rolling stock and motive power in the 1950s to most Central and South American countries as well as to Saudi Arabia, India, Mozambique, Belgian Congo, South Africa, Australia, Thailand and more. Besides export divisions for major builders like Pullman Standard, Pressed Steel Car, Magor and others, the Gregg Company of New York specialized in building unique export railway equipment.
When export freight or passenger equipment was built to the same standards as US equipment, it could travel in trains to the port of departure. A neat modeling idea here using brand new cars.
Equipment built to narrow or meter gauge with different couplers and brake systems would be blocked and shipped on flat cars as loads, often with their trucks if 8 wheeled cars) separately boxed for the sea voyage. Most of these cars went as deck loads on ocean going freighters.
Some non-standard gauge cars, if they otherwise had US compatible brake systems and couplers could ride on temporary standard gauge trucks to a point of export. Their original design trucks would be boxed separately. Such cars were put aboard and blocked as deck loads on freighters as well. For example, passenger equipment for the Paulista and Central railroads in Brazil were shipped that way, with their cars arriving at export docks in US freight trains. Another different freight modeling idea.