His father, Hagop Rossi, was a Catholic Armenian tailor from Smyrna and his mother, Anna, was a Corsican citizen of France.

The family mainly spoke Greek at home, as well as Italian, French and Turkish; Terzian did not learn Armenian as a child.

His students included famous Armenians such as Reteos Berberian, Minas Cheraz, Yeghia Demirdjibashian, Krikor Zohrab, Yerukhan, and other writers and teachers.

[5] When the opera Arshak II was staged in full for the first time in Soviet Armenia in 1945, a different libretto, written by Armen Gulakian, was used.

[6] In 2001, Arshak II was staged at the San Francisco Opera,[7] using an Armenian translation of Terzian's Italian libretto and Chukhajian's original score, prepared by Haig Avakian and Gerald Papasian.