I've used Bitwarden heavily in various browsers and Android. It's really great and very effective at filling in passwords. Every now and then there's a site that does something weird to make it autofill a bit wonky, but I can only recall seeing that happen with registration forms (sometimes the enter + confirm your password fields seem to confuse it). It's near perfect at sign in forms that I've used.
I missed that you said in private tabs. I can reproduce it there but BW also says that private tabs support is still experimental when you try to do it.