Fallen Firefighters Assistance Tax Clarification Act of 2013 - Treats payments made on or after December 24, 2012, and before the later of January 1, 2014, or 30 days after the enactment of this Act, by a tax-exempt organization to any firefighter who was injured as a result of the ambush of firefighters responding to an emergency on December 24, 2012, in Webster, New York, and the spouse or any dependent of any firefighter who died as a result of such ambush, as related to the purpose or function forming the basis of such organization's tax-exempt status, if such payments are made in good faith using a reasonable and objective formula which is consistently applied.