A second's notice is impractical - unless there's already a war underway, you'd be lucky to land strikes within a quarter hour. More likely effective would be counter-battery fire directed by radar, which we (and by extension South Korea) probably do as well as anyone in the world.
The most accurate counter-battery fire in the world can't take shells out of the air, though. Sufficiently well drilled and supplied NK gun crews would most likely be able to fire several rounds each before the first return fire arrived. And even if they weren't, at least one salvo would have to go out for the counter-battery radars to lay their guns at all, whereas the cities targeted by NK in this scenario don't move around much, and could be precisely targeted before the first fire mission commenced.
Twenty million in minutes is implausible. Twenty or thirty thousand isn't, and no preemptive option exists; to even hope to have a realistic shot at forestalling significant civilian casualties, we'd not only have to start the war nobody wants, but do it with utmost ferocity, crossing the DMZ like the Wehrmacht heading for the English Channel.
But even that wouldn't work; NK espionage assets would certainly notice the necessary concentration of force - all they'd have to do would be to watch the news stories about World War II-scale transports suddenly heading west across the Pacific from every military port on the US West Coast - and the NK regime, mad though it be, could hardly fail to draw the obvious conclusion and respond accordingly. There's no way in the modern world to achieve the kind of strategic surprise such blitzkrieg requires - not, at least, without pulling off the kind of deception that Tom Clancy wouldn't have dared write into a novel.