Changing base object name won't help, all you are going to do with base object's stylesheet is to change the content background of that panel.
I did a lot of research and tested a few things regarding your problem and it seems like the only solution is to re-implement the QTabWidget
paint event.
I tried somethings that I haven't read anywhere else and it gave some weird results, this approach should've worked. If you want to study it and see for yourself:
tabWidget->setCurrentIndex(0);
tabWidget->tabBar()->setStyleSheet("background-color: red;");
tabWidget->setCurrentIndex(1);
tabWidget->tabBar()->setStyleSheet("background-color: blue;");