They mentioned the zoo acquired hyaena, gazelle, red deer and chukar as well as some snake species. Recent breeding successes at Mersin - Tarsus AP included three gazelles, two fallow deer, one red deer and one white-tailed deer. BTW: the zoo already boasted of 83 species before the new acquisitions.
With gazelle most probably all goitred gazelle (was not specifically mentioned in the news feature, however most zoos in Turkey have sourced from one of the captive-breeding facilities in SE Turkey). However, there is a population of mountain gazelle in the mountainous south region (allthough I doubt any zoo at all in Turkey holds mountain gazelle) - a recent discovery -. With fallow deer you are making the classic mistake since European fallow deer are by all means a more Mediterranean species, while the more temperate climes the Pleistocene species disappeared after the last Ice Age and was pushed south before the Romans and others started with reintroductions up north (viz also European rabbit). The Persian fallow deer is a species that is more eastern (think Iran, Near East and SE portion Turkey - extinct there -). Deer and gazelle are quite popular in eastern Mediterranean Near East states and frequently these are misnomered as all "deer" (a grammatical transliteration error from Arabic). So, it is not very surprising this zoo maintains white tailed deer (from where? ... Very good question, I am not party to that answer).
I tried to find out about the white tailed deer. But the park hasn't been updating their facebook page since 2019.