The onClose and onClosed callbacks currently only trigger if the alert is allowed to time out and fade out naturally.
If you close the alert by clicking on the close button, or otherwise force it closed via alert methods, they won't fire.
I hotfixed this in my case by adding the following, after line 66 in bootstrap-notify.js (at the end of Notification.prototype.show):
this.$note.on('close', function(){
self.options.onClosed()
})
this.$note.on('closed', function(){
self.options.onClosed()
})