Zoroaster was from Aryana Avijah which was one of the 16 Aryan lands mentioned in the Avesta. These lands which is pretty much identical to Ariana mentioned by Strabo and Eratosthenes extending from Parthia (eastern Iran and Turkmenistan) to the Indus river.
Persia was not one of those nations and was only southwest Iran i.e. the areas around modern Fars. Persians were not even an important people at the time of Zoroaster.
No he is not an Iranian prohet he is a Zorastrian prophet. "Iranian" is a term coined by western historians to refer to us all. No one in Afghanistan every referred to themselves as Irani only whatever the Sassanid empire controlled was called Iranshahr.