My father, a Turk, has a couple of close Armenian friends from Arapkir, a county of Malatya, from his childhood right after WWII. Going back 30-40 years before that period, Armenians were the majority ethnic population in many counties of eastern Turkish cities. Not sure about Persians, but having an Armenian connection in a big chunk of your DNA if you're from the area shouldn't be that surprising.

Fun fact. Yerevan, the capital of Armenia, has Malatya and Arabkir districts.

edit: typo