Hi, baosheng! You've got the general idea right. For your confusion:
他评了副教授 is a colloquial way to say 他被评为了副教授. I don't know why 被 can be omitted here, but it often does in casual conversations.
选 is not exactly the same as 评. If one is "selected" from several candidates, he is 被选; however, if he is "evaluated" by people according to some standards, regardless the number of candidates, that is 被评.
For example, he could be the only one who would go through the evaluation. You cannot use 被选 in this case.