I think the misunderstanding is in a combination of wording + practical application.

Tariffs in the legal sense are technically paid by the importer who sells a product. It's their responsibility to pay it... always.

The importer could technically eat that cost, and the consumer wouldn't see a difference on their price tag.

But what happens in practice, the vast majority of the time, is the importer passes that extra cost on to the consumer by raising the price they're selling it for. This is technically a business decision made by every importer individually, it is not a requirement.

The people saying tariffs are paid by the importer, or tariffs are paid by the consumer, are both right, but within different perspectives and depending on how each importer chooses to handle their tariffs.