Thank you for coming back. No, the desktop notifications work only if the user is using the apps. This is because the notifications are sent to the browser. If you use only the API and have your own APPS web, then you should handle them by yourself.
for example on your page you have a request to your apps web
the apps web calls our api and afterwards you can notify the browser that something happened, but this is a communication between the browser and the web page opened by the browser.