There are rumors Crow came from Oasis, but if he did he never talks about it.
The Twin Mothers tribe is descended from the residents of Vault 29.
In 2250, when Crow was around 12-13 years old and acting as shaman, an old ghoul with a tree growing out of his head came sick and dying on a quest to cure himself to the the Twin Mothers tribe. They took him and cared for him, and Crow helped concoct a potion to save the old ghoul’s life. In gratitude, the ghoul offered whatever aid he could, but the tribe refused, because the “goddess provides.”
That old ghoul was Oasis’ own Harold, one of the original Vault 29 dwellers who’d been wandering the continent since 2290. At his request Harold was introduced to the ‘goddess’ Diana, a projection of the AI which had helped the tribe develop out of ex-Vaulties generations before.
When Harold left Crow figured that was that, until the Legion decimated his tribe toward the end of that decade. Crow began his long, slow travel east, pulled by nothing more than the need to not stop.
After nearly five years of travel Crow ended up drawn to Oasis.
Imagine both their surprises when the new ‘Bloomseer’ was introduced to their god. Crow was always a more skeptical sort. He believes firmly in the supernatural and the power of the earth and nature, but he could see through the projection of Diana and he could recognize Harold immediately.
Crow spent a considerable time at Oasis, learning under the old soothsayer Bloomseer Poplar ways to harness his psyker abilities and use them to their full potential. She could see the future, even if she relayed it in riddles (a trait which Crow picked up from her).
Eventually, he and the Tree Father ideologically clashed one too many times, and this particularly over exploiting Bob and Harold to spread Oasis into the rest of the Wasteland. Birch cast him out, and though there was never a threat of violence and he was welcomed back (as a visitor, thanks to a good word put in by a still grateful ‘god’) Crow didn’t return to Oasis until he brought Mac with him.