I couldn't get notifications to work properly on 8.1 because I knew my Lumia 1020 was bugged (old Band v1 would receive no notifications at all).
So before doing a hard reset, I opted for the upgrade to Windows 10. After that, everything worked like a charm but I receive every email twice on the band. For now I just disabled the Mail tile on the band because the Mails also arrive through "notification center". Keep an eye out for that because that's why I received "every" Email instead of just the VIP ones. Maybe that's why it seems to you that you get every email instead of filtered ones.
Kind regards,