It's pretty much the same as the way in English. はずです is like "Something should happen". You believe something will happen but it hasn't happened. You don't know the result yet. はずだった is like "Something should have happened" as you said. You believed something would happen but it didn't. 晴れるはずです。You believe it will be sunny. 晴れるはずだった。You believed it would be sunny but actually it wasn't. I hope this could be helpful.

I think ”はずだ" means "is supposed " 1). 来るはずです is supposed to come The speaker expects that someone comes here in the future 「今日あいつ来るの？」 「来るはずです 2). 来るはずでした／だった。 was supposed to come The speaker expected that someone came here, but actually they didn't come. 「昨日、あいつ、来なかったじゃん」 「来るはずだったのですが…」 3). 来たはずです。had been supposed to come. The speaker guesses that someone came here, but doesn't know they actually came here or not. 「あいつ、あの時、来てた？」 「来てたはずです」 4). 来たはずでした／だった。 was supposed to come/arrive The speaker expected that someone came here, but actually, they didn't come. 「結局、あのとき、あいつ、来なかったじゃん」 「ちがう！来たはずだったんだ」 ↑ Sorry, I am not totally sure about the explanation for 4.