Timeline error?

Ben took Alex in 1988/89 from Rousseau and looking like a real Hostile. The purge took place in 1991/92, and as we know Ben was wearing the Dharma Workman outfit and working with his dad for the DI. Now, one can say that he was splitting his time between the DI and the Hostiles around the time of the kidnapping. However, if he took Alex in 1988/89, and decided to be her dad, and raise her, it would seem that splitting the time would become a difficulty. To me, something is not squaring up. Not in a cool, Mystery way, but a major continuity error. I am open to theories.

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