I dunno anything about passive barriers, but I know that many begin of battle passive abilities(buffs, clones) goes in the order that the characters are placed/moved(not WHERE they are placed, but WHEN they are placed). I noticed this because it's very important for clone placements as if you have multiple "summoner" (naruto, kiba, kankuro, mains etc) knowing this allows you to control, to some extend, where they are summoned. This is also important if you use iruka with wind dance, iruka first will give you shield while wind dance first will end with 0 value shields.

I can't really see why barrier would work differently, are you SURE it's based on initiative? Have you tested it thoroughly? (different placement location, different placement order)