Because they will price their product to be just a little cheaper than the imported alternatives. This has been discussed to death, with citations, and I believe it to be true. We will see, I guess.
And even if they don't raise their prices to below the imported alternatives immediately, the increase in demand means they'll sell out so quickly, they'll raise their prices anyway
I mean, if their main competitor just got price jacked by taxes, that will push the demand to them. Since they cannot scale up to satisfy the demand, a correct choice is to raise prices. You can argue that this is price gouging, but the easy counter is that this is the market reacting to the taxes and adjusting the going price.
why? local producers don't pay the tariffs.