I haven't used it with magento, but I assume you need to specify a callback url in your magento installation.
In the Google Merchant center, go to settings, then integration, and there is a text box "API callback URL". This should be whatever url that magento uses for GCO callbacks. Without this part, your website would have no record of a sale being finalized in GCO.
If this is already filled in, go to the Tools and then Integration console in your google merchant center and see if there are any reported errors.