Magento version 2.1.10 or above is required.
By default, orders must have the order state of processing for Integration Manager to download them. Note that Magento has both a "status" and "state" field for orders. You can view and map your statuses to the desired state within Magento by going to Stores > Order Status. You can change the state or status that Integration Manager searches for in the Integration Manager Magento settings page.