It is not a bug, but because there are so many things interacting here I do not redirect unless there is nothing else set for a redirect url. If something is set that is where the bridge will redirect you to. It says as much in the user guide and the help in configuration. For the mod_smf_login this will be improved with the next build. For the other modules it is up to them to set the correct data for the redirects.
Either I don't understand something or you. Please - let me understand/clear your understanding:
When I'm logging in from CB login module - after successful login I stay wherever I was. At the same time after successful login from SMF - the bridge redirects me to the main page.
My question: where can I change the SMF redirection to "do not redirect me anywhere, just stay where you are"?
The CB login module works as I want it to work (redirection URL is empty). Why do you write that "I do not redirect unless there is nothing else set for a redirect url. If something is set that is where the bridge will redirect you to". So where is the bridge checking the redirection URL if it is not CB?