I honestly think that is just bad wording for "When you make a group, certain classes have abilities that other classes don't have. It is important to have a varied group composure to optimize the individual abilities of each player."
Elements are a general version of "Elements of a group."
I've been in groups with all sorts of players of all class combinations, and never have I seen a "magical effect" appear on an opponent that hasn't come from one of the players. I think it just means like if you have 2 Warriors, their bleeds count seperately, but if you have many Mage/Scout in your party, their Fire Rose will count as only one Fire Rose debuff on your target. Or if you have a Mage and they use Elemental Weakness on a target, all players that cast magic damage on the target benefit from it.