To opt-in to this behavior, follow the steps on that page:
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Sign in to the Amazon Cognito console. If prompted, enter your AWS credentials.
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In the navigation pane, choose User Pools, and choose the user pool you want to edit.
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In the Sign-up experience tab, choose Edit under Attribute verification and user account confirmation.
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Choose Keep original attribute value active when an update is pending.
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Under Active attribute values when an update is pending, choose the attributes that you want to require your users verify before Amazon Cognito updates the value.
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Choose Save changes.
This will enable what should be the default behavior for user pools: The attribute will keep its old value until the user actually verifies the new value, at which point Cognito updates the value to the new one.