The Network tab in the Google Chrome Developer Tools window shows almost all http requests made, but does not seem to capture anything when the http request results in a file being downloaded.
How can I capture download requests in Google Chrome?
I am sure that your file download is happening by opening a new window. Network tab of developer tools only captures the request of current tab.
For example, following link will download the file but it will not appear in the network tab.
<a href="/yourfile.doc" target="_blank">Click Here to Download file</a>
Similar type of things can be done using javascript using (window.open, dynamic hyperlink/iframe), which will not appear in the network tab.
Various Javascript approach you can check here
I have observed similar behaviour in my past.
You can check the chrome://net-internals in older version of chrome and chrome://net-export/ in the newer version of chrome to monitor any type of request being made by any instance/tab of chrome.
Note: You can check the internal events of chrome by typing chrome://net-export/ in the url box of chrome.