It's just that the AI plays it this way. Try using Kankuro second round a lot of time (on manual mode). Then the AI will start using Kankuro before main

Well, as I said, just showing the AI your preference worked for me when I wanted Karin not to be used first round. Could have been a coincidence though, need to try it once more

The team was the same :) I used Midnight with Lightning Armor but at first Karin was always used first round, in auto, but played main manually for a while and then on auto it started using Midnight first. Could be a matter of equips maybe...