This is something I recently ran into, and thought I'd share, in case anyone encounters the same or a similar situation.

We're rolling out Office 2016 Standard (not 365), and so to make it a smooth installation where the end user doesn't have to do anything, I created an .msp file with the Microsoft Office Customization Tool.  It installs well, sets the right settings, &C., programs work fine after.

After the rollout began, we got a few complaints from users saying that after the upgrade to Office 2016, they were no longer receiving the Desktop Alert/toast messages when a new email arrives.

In looking into the matter, all the users who reported it were running Windows 10 version 1709.

Internet searches revealed that there were a lot of complaints about notifications, mostly related to email, and (I believe), all Windows 10 version 1709.

I tested this theory, and proved it to be true.  Using this Office installation method, Windows 7 and prior versions of Windows 10 all get notifications.  It is only 1709 which does not.

While I can’t find any documentation from Microsoft themselves, this company references changes to the way Windows allows programs to display notifications in their KB: https://knowledgebase.macrium.com/display/KNOW7/Windows+10+Notifications+-+1709+Fall+Creators+Update

"Prior to the 1709 Fall Creators update, the Windows 10 'Notification & actions' settings dialog would show duplicate and redundant application icons in the 'Get notification from these senders' list of apps. Apps could hang around for weeks after uninstalling and this led to usability issues and confusion. This problem wasn't limited to Macrium Reflect, it was a generic design issue and was widely reported.

The Windows 10 Fall Creators update has attempted to rectify this problem by restricting the apps that appear in the list, but has perhaps gone a bit far. It appears that the list now only shows apps that are running AND currently have an icon visible in the Notification area of the task bar. As soon as the icon is hidden it's removed from the list."

But it appears to be restricted even further than that. Our images have all icons visible in the Notification Area of the Task Bar at all times, and even with Outlook open, it still does not appear in the list.

What I found

To make a long story short, what was causing this issue for me was that in the customizations, I had moved the Office 2016 Start Menu shortcuts into a folder called "Microsoft Office 2016" (like prior versions have had).  When I removed that setting, and left the Start Menu shortcuts in the root of the Start Menu, Desktop Alerts/toast messages of new emails arriving worked on Windows 10 version 1709.

However, while this fixed subsequent installations, it does nothing to fix prior installations.  Moving the icons back out of the folder did not allow Outlook to display those notifications.  The only fix for prior installations was to uninstall and reinstall using the corrected method.

Summary

To be added to the "Get notification from these senders" list in Windows 10, Outlook 2016 must

1. Be running
2. Have the Outlook icon visible in the Notification Area of the Task Bar
3. Be installed with icons in the root of the Start Menu

This works for a new install, but if Outlook does not show up in the "Get notification from these senders" list, Office must be uninstalled and reinstalled.

Now, of course, this is anecdotal evidence, and based on my specific situation, but given the number of posts complaining about missing notifications in Windows 10 on the Internet at large, perhaps someone will be able to find this and apply it to theirs.

Good luck.

This is also posted on Spiceworks.