Alexander went to Siwa in 331 BC, having just founded Alexandria, and crossed several hundred kilometres of desert to do it. That much is agreed. Almost everything else about the visit is a reconstruction, and the reconstruction is doing more work than the evidence supports.
The problem is the sources. Nothing survives from anyone who was there. The accounts we have (Arrian, Plutarch, Diodorus, Curtius, Justin), were written between three and five centuries later, and they draw on earlier writers whose work is lost, including Callisthenes, who accompanied the expedition and whose job was in part to present Alexander well. The surviving versions disagree about the route, about who went in, about whether Alexander consulted the oracle alone, and about what was said.
The tradition that the priest greeted him as the son of the god, and that this confirmed Alexander's divine paternity, is the version that has come down. It should be treated with care for a plain reason: it was useful. A ruler claiming Egypt benefits from the senior Egyptian oracle acknowledging him, and the writers transmitting the story were working within a tradition that had already made Alexander more than human. Some ancient accounts say frankly that Alexander never disclosed what he asked or what he heard.
There is also a quieter possibility that gets less attention. Consulting an oracle was a normal thing for a Greek commander to do, and Siwa's reputation in the Greek world was long established, Athens and other states had sent to it, and Herodotus knew of it. Alexander may simply have done what a Greek of his standing did before a campaign.
This entry reports that he went and does not report what he was told, because the second thing is not recoverable. The temple at Aghurmi still stands above the palms, its surviving inscriptions of the fourth century BC. Siwa today is a Siwi-speaking Amazigh town of some twenty-five thousand people. The oracle's cult has no living continuation, and nobody there claims otherwise.