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When upsell offers are presented to customers at checkout, the order fulfillment status is set to On hold until the customer completes their order.
When an order is On hold you can reserve inventory for the order, but you can't fulfill the order until the fulfillment hold is released, and the order fulfillment status changes to Unfulfilled.
On hold status will be reverted if any of the following happens:
* The customer accepts the offer - the item is added to the original order, and another payment is issued.
* The customer declines the offer - the order is marked as unfulfilled
* 60 minutes pass (1 hour) - the order is marked as unfulfilled
This process is not app related. It's managed by Shopify. You'll get the same result with any other post purchase one click app.