A guide would be pretty neat. :)
I checked the first battle, and the cause of that EXP jump is how I calculate level-ups and some tacked-on rebalancing. This'll happen for the first level-up from 1 to 2, and the real first level-up would be at 85 with the rebalancing, but it used to be 20, and that is still the default set when starting a new game. Other characters don't start on level 1 but are set to a pre-determined level in the background once you get them and won't have that first experience bump. It's an easy fix and it'll go into the next update. Won't affect anything gameplay-related.