Well, you see, the confusion appears to stem from the use of the term "turn." The attack cards aren't referring to a player's turn during the battle, but rather the turn of the player who started a battle. It might be easier to explain it this way:
1) It's the start of your turn. You flip up a Location card, choose which creature you want to attack and which one you want to attack with.
2) Battle ensues.
3) After the battle, you have the option to move other creatures of yours to empty spaces. After that, your turn ends, and this is where the temporary stat decreases would end. Then it would be your opponent's turn.
So you see, since battles are always entirely within a player's turn, technically the status effects last for the entire battle. So, you play a card like Rip Tide, which would then limit your opponent's ability to play cards that stat check or challenge Courage
for the rest of the battle.
In girum imus nocte et consumimur igni