Neither South Korea nor Japan are retliating and they sent delegation to "negotiate", which in context means to see what concessions they can offer to try to remove or lower the new tariffs.
That's pretty much "caving in", but that's also expect: Both countries are not strong enough and too dependent on the US to do otherwise.
The EU is not yet retaliating (the tariffs mentioned in the article are retaliation for the US's steel and aluminium tariffs from last month, not the most recent batch), and is negotiating; as I mention there was a zero-for-zero option. Retaliation for the current round of tariffs is currently under discussion.
Make no mistake, it'll be the same in Japan and SK. At least the credible threat of retaliation, if not retaliation already in action (the China approach) is required for any real negotiation.
That's pretty much "caving in", but that's also expect: Both countries are not strong enough and too dependent on the US to do otherwise.