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Cu_xBi₂Se₃ is a topological insulator (TI) material in which Cu intercalation between the Bi₂Se₃ quintuple layers can yield superconductivity. Using ambient-pressure X-ray photoelectron spectroscopy (AP-XPS), we report copper migration from the bulk towards the surface in this material in controlled oxidizing environments as well as ambient conditions. The migration occurs on a timescale of hours to weeks after initial cleaving, and proceeds along with the oxidation of the sample surface. These results demonstrate dynamic surface chemistry, relevant for tailoring the topological surface states for utilization in ambient environments.