There is no problem with “expected” nor with “… would have expected… ” The problem is in combining “notified” with "expected".
I think what you want to express is that something happened; you thought someone should have told you about it; that person did not tell you about it. Is that right, please?
The simplest way to say that would be: “I expected you to notify me” and there are others… “I expected to be notified" or “I expected notification” for instance, among many including fralau’s “I had expected that you would notify me.”
Certainly “I would have expected you to notify me" does convey the sense of an opportunity that has already happened, because you used “had expected…” and yes, that sentence is designed to be used to express both the expectation and the notification, as well as the problem, being in the past.
“… in the past” here means a continuous past, from the time of the event until now. “I would have expected you to notify me" could only include the future in a vague conditional speculation.
“… just when the problem was happening” can only be expressed by an extra clause, as "I expected you to notify me at the time/when it happened…”
If you expected the person to notify you in the future, whatever happened, you would need "I expect you to notify me”.
If you expected the person to notify you in the future, on condition, you would need at least “I expect you to notify me if…” and perhaps, yes, “I would expect you to notify me if…”
One could indicate that one would have expected a person to do something in the past with, for instance: “I would have expected you to do something…” in which case adding “… in the past” would do no damage but neither would it be in any way necessary or helpful.