Re: Why mistake happened in the workflow didn't notify the responsible role I assigned ?
I do not have an instance in front of me and I can't read the text in these images, but I'll try to help. There is a chance that this is a bug in the OOTB stuff, but let's first make sure you you have your template/process set up correctly.
Are you positive that you have a principal assigned to the Manager role?
Are you positive that your changes are reflected in the running process? Have you checked in your edited workflow template? If you are are calling this workflow from a Lifecycle Template, verify that the UseLatest flag is checked. Also verify that you are editing the workflow in the correct context. An easy test may be to edit the name of the activity, check it in, and refire, ensuring that the exception is thrown again.
Assuming those things are correct, Does the process template have a field for Responsible Role? I would try changing that to a third/different role, just to see what happens.