I was watching the movie "The Promise" yesterday (Starring Oscar Isaac and Christian Bale). The film takes place in the Ottoman Empire during the Armenian Genocide. For some reason, everyone was calling the city Constantinople. From my understanding it makes sense for Christian Bale's character to call it Constantinople (he plays an American journalist), but I thought the Armenians would have called it Istanbul.
Well, the name of the city was Constantinople and that name remained in use for hundreds of years after its eventual capture. Many people living in Asia minor and the surrounding regions actually referred to the city as "The City" which is actually where the name Istanbul comes from: "Eis ten polen" or Into the City, which is how many Greek speaking subjects referred to it. The city has gone by many different names and different people would have used different words to achieve different ends.
Apparently, the term root of the modern word Istanbul is first attested to in Armenian sources ("The Etymology of İstanbul: Making Optimal Use of the Evidence" Woodhouse/Stachowski), I think that Armenians probably would have used Constantinople or the city, or as you guessed, some variant of "Istanbul" at the time.