It depends on the specific wording of the feature, but many effects which add damage to one damage roll, such as the School of Evocation's Empowered Evocation adds the damage to each dart since it's one damage roll applied multiple times, just as if you applied the Empowered Evocation to Fireball and then struck multiple targets. It's not entirely clear if this was how the rule was intended to work, but based on Jeremy Crawford's other rulings, that appears to be the answer, and Jeremy Crawford has ruled that Empowered Evocation applies, but he wasn't specific about the math. Some similar features apply a bonus to damage to one target affected by the spell, in which case you would pick one target struck by one of the missiles and apply the damage bonus only once.