The verb (both Imperfective and Perfective aspects) is reflexive, so he shaved himself. Both aspects are also intransitive, which means they can't take a direct object, so you can't use either to say that, for instance, "he shaved his brother". For that, you'd need to use the transitive forms of the verb-pair, бри́ть / побри́ть.
"He shaved yesterday" means "Он побрился вчера". As I know "брился" and "побрился" not the same.
They both can be used depending on what you mean. If you focus on the fact that he ALREADY shaved yesterday (so he does not want to do it today) imperfective does the job. Or perfective, because a grown man without a beard is expected to shave every few days. So, saying that he DID is not going to raise any eyebrows (shaved? really? did we ask him to?)
If you rather want to pin the action of shaving on "yesterday", expressing the sequence of events, побрился is the only option.
I couldn't find a space to reply to your last explanation starting with "already" - but it seems to me that if in doubt use the IMPERFECTIVE because it seems that one can always find a rationale for justifying the imperfective even when to we English novices the justifications seem to be stretched. I'm not saying the justifications are not valid but to those of us not steeped in the Russian language they seem extremely subtle. I am wondering if there is any systematic way of learning these subtleties or would you agree - it's best to use the IMPERFECTIVE if in doubt.
So the imperfective is saying that since he shaved yesterday he is still clean-shaven enough today? Would that be it? If I did somethinhg yesterday and the result still continues today, the imperfective works even though the initiating action was a one-time finished event?
"already" is one of the interpretations. It is a case of a more general use for making a reference to an action as a fact regardless of its results and inner structure (e.g., "When was the last time he shaved?").
Perfect and perfective are completely different things, so trying to apply the rules of how you use English perfect tenses to the use of Russian aspect (and vice versa) will only confuse you. They rarely match.
Whereas perfective has quitea narrow field of meanings, the imperfective aspect combines many meanings, which also depend on the meaning of the verb and you realistic expectations of such an action. It is no wonder that the interpretation of random sentences is difficult.
Он бреется вечером.
You can also use a slightly different structure that is taught later in the course. Instead of saying you do something "in the morning" or "on Monday" you can say that you do it "mornings" or "on Mondays". It is по + Dative plural:
- По пятницам я вообще не работаю. = On Fridays, I do not work at all.
- Я бреюсь по выходным. = I shave on weekends
- Я бреюсь по понедельникам
- Я бреюсь по вечерам.
We use this structure for days of the week and times of day.