Multiple references are made to Persians worshipping at the religious sites of Greek gods and making sacrifices there. In particular, Cyrus, brother to the king of Persia, references the Persian Orantas’s repentance at an altar of Artemis before chastising him. Curiously, he cited Orantas’s later betrayal in spite of this repentance as further evidence in favor of his execution. Orantas is described by Xenophon as a Persian noble related to the King. Were the native Persians true Polytheists, or were their general religious practices more nuanced?
To start, I go into the general features of Zoroastrian theology here. I will have a look at my sources and see if I there is enough material to put together an answer adressing more specific to your question. The problem you face here is that there are very, very few native sources for the Achaemenid period, so don't get your hopes up too high, but I will see what I can do. Also, feel free to reply with any followup questions specific to the linked post.