nUI should automatically change action bars so I suspect there is another setting that bartender addon knows about that nUI doesn't. hopefully it is easy to find.
Edit 1: I was posting those example links to help explain that it is a blizz fault that is likely causing it as it was happening without any addons for someone.
Edit 2: Unfortunately I can't see what setting nUI needs to make as I cannot locate the settings in bartender that even remotely looks like how nUI sets its bars up with. And without an easier way of testing I can't even play with it to track down the setting like I did with all the other possible settings.
Edit 3: Looking at the blizz coding it is possible that it is linked to the following which may or may not be in nUI .
Lua Code:
elseif (HasTempShapeshiftActionBar()) then
MainMenuBarArtFrame:SetAttribute("actionpage", GetTempShapeshiftBarIndex());
I will try and take a look before I start playing tomorrow.