With that option unchecked, mine doesn't show any popups when I play a file from Windows Explorer.
If yours does (and you're running the latest version) you might have post a bug report.
Damn I am sorry, I worded it wrong.
I do actually not get a "regular" pop-up notification, what I meant is that when I click a new song from Windows Explorer, then in my Window taskbar, that in my case is hidden, becomes visible and the MusicBee icon in Taskbar flashes, and that is what I consider annoying.
So the problem is if MusicBee's developer can add a preferences setting or it is a Windows OS thing.