First Turkey is in violation of article 1 (The Parties undertake, as set forth in the Charter of the United Nations, to settle any international dispute in which they may be involved by peaceful means in such a manner that international peace and security and justice are not endangered, and to refrain in their international relations from the threat or use of force in any manner inconsistent with the purposes of the United Nations.) of the NATO treaty by not seeking to solve the Syria matter by peaceful means. It continues to provide a safe haven for the FSA mix up (including elements of international terror organizations) and is violating Syrian air space to provide these forces with intel. NATO is a defense organization and treaty not an offensive one. Turkey is already engaged in war with Syria by hosting an army it owns it and its actions. As such Turkey is engaged is a foreign act of aggression. (UN provides for states to act in self defense as Syria did however the treaty does not get very in depth about first strike responsibility and appears to be a moot point)
Second the plane was in Syrian or international airspace. This is not covered by the treaty which specifies the attack needs to be "on or over" their territory.
Third the North Atlantic does not need to have security restored and the Mediterranean security is not of concern in the treaty out side of the territorial waters of the states on this body of water.
This is not a NATO treaty matter of obligatory use of military force.