So this one came up last night. Tactical Marines are doing AOE (1) to 3 units. Damage is assigned and dealt simultaneously (no shields played). Can Fury of Sicarius then be played in response to the damage to destroy all that were damaged?

The card reads: "Reaction: After a [space Marine] unit damages an enemy non-warlord unit by an attack, destroy the attacked unit."

No. The Area Effect section in the RRG confirms that doing an Area Effect is not doing an attack (instead, it's a card effect), and therefore this doesn't satisfy the "by an attack" criteria. "By an attack" doesn't mean during an attack, it means the actual attack (ie applying its STR).