I personally stay away in exams from material not covered in assignments or tutorials, simply out of fairness rather than by a policy requirement. Once can always argue that, if it’s in the course description or the syllabus, it’s also fair game even if not covered in class but to me at least that’s over the line.
There has to be some flexibility to allow instructors to go beyond what was strictly in the lectures: in an absurd example one could argue that, if the instructor showed in class how to multiply 3x5 but not 4x7, then the first example would be legitimate a legitimate exam question but not the second.
A reasonable boundary is to expect that topics covered in class - rather than specific material covered in class - are fair topics. In the example of my previous paragraph, both are examples of multiplication so both would be fair questions in my mind.
Thus, it is possible to have an exam question on the Poisson distribution if the question deals with properties common to distributions rather than a unique property of the Poisson distribution, provided that distributions were a topic covered in class or tutorials.
I do not know examples where allowing exams questions not covered in class is a policy. I know of plenty of instructors (including myself) who make it a habit of not asking in exams the same examples covered in class, although the exam questions are on topics covered in class.