Have you tried using auto with neji?
On auto mode, neji will either cast before the second normal attack of your team OR at the moment enemy attempt to cast. So if an enemy is trying to pull a "suprirse mystery" on you, neji can get him on auto mode.
Provided that you do not have other msyteries that are competing for your chakra on that turn.

Auto is a useful and tricky tool
This post was last edited by 117***@google at 2017-2-15 04:48

that would only work if he or she knew which turn he is going to cast it

I tested it out and sasori seems to be casting third round.