Not necessarily.
A tariff increase the cost of a foreign made good either by country or universally.
When dumping is taking place then the tariff simply removes the offending country to reduce it's price by the amount of the tariff if it wants to continue to have US consumers. So then the offending country pays that tax by adjusting it's price or devaluing their currency.
Tariffs can also be used against Human Rights violators to balance their use of slave type labor as a tool to remove the incentive.
Protectionism is a different case. In that case the consumer would be asked to pay for the inefficiencies of domestic manufacturers.
Retaliatory Tariffs - are used as payback for the offending country putting tariffs on our products.
In some cases (mostly China) have actually used export tariffs against their own manufacturers to make sure that US manufacturers of the finished products could not use the Chinese product to compete against Chinese companies manufacturing the finished products. This was mostly due to their devaluation of their currency making all products globally cheap.
Our industry has been a victim of export tariffs. You can purchase the finished good from China cheaper than you can buy just the raw materials from the same sources in China. Turns out they put export tariffs on the raw materials to try to kill off US manufacturers.