I am sure the formation of the welt may play some part, but the main reason for the echo effect has to do with how the nerves work. The sequence of events is like this: The cane hits, and the appropriate pain nerves fire, sending their message to the brain. The subject feels intense pain. Now, once nerves have fired, they cannot do so again until after a recovery period of a few seconds. When this period is up, since there is tissue damage at the site, they fire again. The echo may hurt more than the original, since nerves that have fired and recovered are hypersensitive for a brief time.
Now, there are several types of pain sensors, each reacting to a particular type of stimulus, shuch as pressure, heat, etc. Most methods of inflicting pain affect only one type. The reason electricity is so effective as a torture method is that it has the ability to fire all the pain nerves at once. Also, it does not damage them if used properly, so a few seconds later they are recovered and ready to fire again. If the shocks are timed exactly right they will hit just at the hypersensitive period.