Thank you very much for your post.
It is very difficult to understand how your system works. ATUM is WC extension and only works with stuff WC can see.
I guess those orders are external products and those products have no stock in WC. If so, we can't know if an Amazon referral link is finally sold when following it or not. That would need to communicate with every site's API (if any).
ATUM does not work with orders, we work with inventory. Is the inventory held in WooCommerce and does your eBay, Etsy, Sears and other sites discount inventory in WC?