Arena battles or matches are AI controlled in Brave Frontier. The game system decides each unit's action based on a set of parameters during the match.
It is more easily explained that Brave Burst execution is random or AI based and the developer nor the end-user has control over it while it is happening.
This is the current system for the Arena feature of the game and is constantly improving or evolving as time goes by, in this regards some future changes can be expected if the developer decides to improve the mechanics along the way.
For a more detailed explanation on how AI behavior works in-game check out the Arena Types of Units and how it can influence the activation of Brave Burst here.