The BRB makes a couple different references to turns:
Game Turns - Contains 2 Player Turns. Player Turns - Contains the phases in which we do things. Turns - as per page 12 BRB it means a Player Turn
Looking at it from this view point, it would make sense and your opponant could demand that it is rolled at the start of each Player Turn. That is if it wasn’t for the EXCEPTIONS(BRB P12) paragraph, since the rule doesn’t say what order it occurs in on your opponants turn, which the EXCEPTIONS rule says needs to be there for it to work on the opponants turn.
This leaves me to think “oh great, another poorly written rule…”.
In France, we too believe that it’s game turn (they precise “game turn”), but I personnally think that it’s at the start of the second turn, no matter which player begins : The CD player begins : its own turn. The opponent begins : the opponent turn. So, I make sometimes the Toughness test at the beginning of my opponent turn if he has begun, and later at the start of all its turns… Am I right?
Yeah, it’s the start of the turn, whoever’s turn it is. Which is a bit daft, because it means you might be testing for something to happen to your models in your opponent’s turn, which goes against most conventions in Warhammer. It probably ought to be "at the start of the controlling player’s second turn, and every one of his turns afterwards…"
It's referring to game turn. It sets the precedent at the start of the sentence. Therefore, you only test at the start of your own turn.
I think Tommy H is right, as it makes sense, but the rule is really pooorly written. Check the sentence:
"As a result, from the second game turn onwards, at the start of each turn a Toughness test must be made for each K'daii unit"
It's clear we have to test from the second game turn onwards but we have to test at the start of each turn. Reading the BRB p.12 they say (at least in Italian): every time a rule specifies turn it refers to the player's turn!
Am I not getting something?
I will continue to use at the beggining of the second Game Turn onwards as it makes sense and this is the general consensus but honestly I'm not sure the rules states this... :(