QTTabBar user also here. If it helps, my Ctrl+N behaves the way Neil describes, so it's not a compatibility issue.
I use Groupy to autogroup both PowerShell and the Command Prompt. Normally both open in C:\Windows\System32, so I always used my own shortcuts to have them start in my desired working directory. The + button uses the system defaults again, so I had to do some tricks to have them both start in my normal directory again using the +.
An option to set a default working directory for anything started by Groupy would not be a bad idea.
EDIT: Note: I use the original QTTabBar from Quizo, not the abandoned open source fork.