This could be a suggestion

I've heard that auto prioritizes attacking over defensive mysteries.

I'm reluctant to suggest refining (thus increasing initiative) since I don't know if it works and runes are expensive, but it might..

As said above attack is prioritised over defense skills while on auto. You have some options though.

1: Use someone, like Asuma or Temari 3*, that adds an extra 20 chacra at the beginning of the fight. Asuma would be best because Temari will just use her added 20 to attack anyway.

2: You might want to add normal Neji or GNW Neji in place of Hinata because their defenses are for the most part automatic Or if that doesnt fit what youre trying to do then you'll have to make an auto specific team.