Right, but they'll underprice just below the floor price for the imported good, because why would businesses leave money on the table?
The choice for consumers won't be "choose between a $5 item and $15 item" it will be "choose between $13 and $15", like I mentioned above.
This doesn't work as easily if the sticker price for the imported good is $5 and the real price displayed at the end of the purchasing funnel. The local business will have to keep its sticker price at $5 to avoid losing customers when they initially compare goods or rely on customers to come back to them once they get faced with the tariff tax, which will also lose customers.
For goods that have alternatives, businesses may choose to under-price (relative to their tariffed competitors) in order to gain sales and customers.