I took a look at this replay, and if you look closely, Tendo's all move after Earth Mains (Tendos are move 2).
Concerning Chojuro, I'm not sure where was he in this video, if he was at all.
If you believe I missed something, please let me know, but this does not seem like a bug.
It might be hard to tell by replay cause it looks slower here but in game the Tendos fire instantly. Look at 3 light mains after snake dies, the enemy team does all their normal attacks while they don't move at all, even their move 1s who are all faster then enemies. The game just fast forward through enemy team actions, like the really fast guys you meet in seal/ninja exams.
As for Chojuro, he is not in this replay but i thought he is a well known one, in same situation after Snake dies he will attack three times. I think it's because of his extra atk buff, he never looses first, so when the team re-applies their buffs after snake dies he gets another one.
https://www.youtube.com/watch?v=toDdWzsg2go Here is video at 8:20 and 8:50 you can see it in action.