But why would they if they don't have a competition on price without a tariff?

Why wouldn’t they have competition?

Even if you assume perfect competition costs like tariffs can be passed back to producers.

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