I import stuff so I have actual experience, before my goods arrive at the port my customs broker needs submit paper work showing that it is and it's value. At that point any tariffs are add to the bill for entry and I have to pay it, that tariff becomes part of my cost of goods which I factor in when working out what I charge the customer.
Same will happen in America, the importer pays the tariff and if the don't pass on the cost to the consumer they make less money and/or lose money.
Exporters do Not pay the tariff, the reason Tariffs are bad for exporters is it make the product more expensive in the country that imposes the tariff which can effect demand for that product