Imagine a demand and a supply curve. From the perspective of a producer outside the country the tariff effectively shifts the demand curve, but doesn't affect supply. That's going to lead to a lower price at equilibrium.

Of course, from the perspective of the consumer it's the opposite situation, the supply curve shifts which leads to a higher price at equilibrium.

Both happen simultaneously, who pays most of the tariff depends on the elasticity of the supply and the demand

For example, if there's a 35% tariff on a $100 item, the importer technically owes $135. But the exporter might lower their price, maybe selling it for $70 instead to help offset the tariff and keep the business deal going. In that case, the exporter is basically covering part of the cost. On the flip side, the importer might just raise the final price and make the customer pay more...or better yet, assume the cost due to intense local competition.

So even though the importer pays the duty upfront, who actually feels the cost depends on how the parties involved respond. That's why it makes more sense to say someone in the supply chain pays. It's not always the same person every time.