There are 3 things that take precedence about who attack first.
1. Prompt Skill
No matter if u are faster n have 1st movement of the enemy, if u dont have prompt skill then the enemy will attack first.
2. Movement
If u have prompt skill then u must have movement 1. No matter if u have prompt skill n great initiative but u are in 2nd movement, enemies who were in the 1st movement will attack first.
3. Initiative
If u have condition number 1 n 2, increase your speed then u will be faster of the enemy.
But in the case of arena n trial, many ppl argue initiative will be ac*ulate from team but i doubt it.