Well, maybe if their leader would be a little nicer and respect border agreements and stop attacking ships and bombarding people on land the South Koreans wouldn't have to fight back.
Well, thats a different story because you know for a fact the US will crush Mexico and so it would be smarter to go north, but not to Canada. In North Korea its a different story because one its obvious North Korea is going to lose if a war does break out. So would I rather run North while I have planes and tanks following close behind me. Or would I rather run to the people who are (as you said with China) required to help refugees and is a shorter distance. And you got to think that this refugees while the battle is going on around them they are just going to go to somewhere where they can be shield from the gunfire and bombs being dropped. They aren't going to run in either direction untill the bombing stops and the gunfire stops. Now, say if South Korean's troops pushed North Korean's troops North would i rather follow the armies fighting to China or would I rather go to South Korea. However, if the North Korean army pushed back South Korean army I would then go North, but not as far as China.
It really depends on who won the intially fight that would decide where the refugees would run.