I'd rather he didn't hire this man.
I'd rather he had not hired this man.
A native speaker said both are correct. But the second one sounds like I have to put a verb in Simple Past in the end. Like in this situation:
I'd rather he had called me before he paid me a visit.
Best Answer
If the question is, are you correct in assuming that your last example is correct, "I'd rather he had called me before he paid me a visit," then you are correct.
If you were to use the simple past in your example sentence, "I'd rather he called me before he paid me a visit," that would mean that you, in general, would prefer he called you before visiting, and that it's occurred at least once in the past. The use of past perfect makes it clear that you're talking about one action that preceded another single past action.