Processing - DropStream will import all orders with status Processing. DropStream does not send an acknowledgement status update back to Magento. The order will retain the Processing status until the order has been shipped.
Complete - DropSteam will send a tracking number to Magento when the order is shipped, and will update the status to Complete.
You can configure DropStream to send email notifications when tracking numbers are available.
View this article to Set Email Notifications for Magento