It's not "either/or."  

An attack on North Korea would certainly be answered by a holocaust on South Korea, with missiles hitting Japan too. We have troops there, and on Okinawa, and South Korea, and the 7th Fleet is vulnerable. The South Koreans realize that a war will leave them toast,ed and that Trump is incompetent, rarely considers the potential consequences of his actions in any sphere, so they have good cause to be frightened. 

Trump's answer so far, by the way, has been to Japan and South Korea, "pay us more for your defense, or we'll take it away," and, "Japan should have nukes, too."  

Bill Clinton, for all his faults, did a lot to contain nuclear proliferation. Bush II, not so much and Obama not much better. 

Trump thinks that the ten minutes he spent with Premier Xi will keep everything under control. He's not exactly a rocket scientist.

The North Koreans, from the rice farmers to the generals, have been fed propaganda for three generations. The don't know any better.