First of all, let's use proper English.  There is "Turkic" as adjective and there is "Turkic people" as noun in modern English. There is no "Turkics" in English as a noun.  Azerbaijanis by far is the rightest terminology.  If you want to emphesize the ancient periods, Azerbaijani still should be fine, because "Azerbaijani" is a new term for Turks who used to live in old days.  Only Azeris have lived in or near modern Armenia.  Kars, Igdir which are in Armenian border of Turkey are all populated and used to be populated by ethnic Azeris (and then some Kurds).  There is no known fact of Anatolian Turks living in or near modern Armenia.