When I do /vanish am invisible but can recieve private messages.
When I follow with /vanish toggle nochat am getting confirmation message that command worked but still getting private messages - why?

Using:
bPermissions - v2.10.1
VanishNoPacket - v3.18

Its bChatManager, familiar with that?

Whatever plugin you use for messages doesn't respect the bukkit visibility API. As for nochat, that just blocks you from accidentally sending messages.