In general there are two main sources of latency steps.
- Long distance links.
- Congestion resulting in queues.
Many networks contain routers seperated by large geographic distances, so yes it is absoloutely normal to see large steps in latency within a network.
If you see the expected step in latency for an intercontinental connection but not at the expected place in the trace, the most likely explanation is that the routers were not where you thought they were. IP addresses and reverse DNS hostnames only give a weak hint as to the physical location of the device they are assigned to.
Specifically I expect that your korean provider has a router that is physically located in the US to give them more flexibility in purchasing onward conncectivity, but you were unable to correctly identify the physical location of the router from it's reverse DNS name (either because the information was not there, because you were unable to figure out what the name meant or even because the information in the name was flat out wrong).
(if you see a hop with higher response times than later hops then that indicates slow ICMP generation or inconsistent routing but if the response times are consistently increasing through the trace then the latency is most likely real).