If you created your own Core Prefabs you can specify the battle transition inside MyGameCore. The object BattleManager contains a component called BattleTransitionController which holds a reference to the DefaultAnimation.
The referenced prefab contains component called BattleTransitionAnimation that controls what happens during the Enter & Exit transitions (e.g. plays an animation)
To create your own transition. Create a prefab variant of BattleTransitionAnimation and check BattleTransitionAnimationBands as an example. Then replace in MyGameCore BattleManager component.
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Make sure that if you use an animator you set its UpdateMode to UnscaledTime
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