The Legends ultimately invited Zari to join the crew, and Amaya in particular was interested in her totem’s seeming connection to Zari’s.
That said, judging by Tala Ashe’s comments to EW, signing on with the Legends doesn’t mean that Zari will be a time traveler like the Legends.
When Zari made her Legends of Tomorrow debut, she was being hunted through a dystopian future in which ARGUS has outlawed all metahumans.
Her brother was killed by ARGUS as a meta, and so she tricked Sara and the other Legends into helping her break into the metahuman prison to steal back the totem that had been taken from her brother when ARGUS captured him.