Quote from rulebook: "If two or more required actions are occurring at the same time (for example, more than one "start of turn" action), the Free Peoples player decides in which order they occur."
Since both Treebeard and resolving damage are required and come from the same trigger, the Free Peoples player can choose whichever best fits their strategy: Treebeard first to try and kill the uruk, or damage first to force the shadow player to exert other minions.