Guild Wars 2

Do I need to be ON my revenant for the mistward collection items to drop? Like, for example, on the world bosses etc? Or will the items drop on any character?

In short, no.
The items will drop regardless of the profession your are using.
However, once you have the last piece of collection and unlock the armor, be sure you are using the revenant. The newly unlocked mistward armor is soul bound on pick up.

Just noticed it sadly and lost my Mistward Pauldrons to my Warrior. I hope to God that ArenaNet is going to change that armor to account bound, or at least make it bind on equip, as it doesn’t make sense to make it bind on unlock since a lot of people will unlock the full set on their other chars and transfer it to their newly created Revenant that isn’t geared up yet.