It is possible that the other characters will have other checks in this round. 1) Barriers that summon monsters for characters to fight or affect all characters at the location. 2) Multi-check banes, like villains, where the 'current turn' character only need attempt one of the checks, but the other characters there can handle the other check(s). 3) Recharge checks, such as on items or spells (Lem casts 'strength' to help fight the monster, but has a penalty added to the recharge check for failing the wisdom check).
It is 'turn' rather than 'round'. PACG doesn't seem to know about rounds. But you're quite right. If any of the non-active characters (at the active character's location) fails the Wisdom 6 check, AND needs to perform a further check within the active character's turn, they suffer the +1 penalty. It could be annoying, but at least it doesn't persist.