I don't think that rule holds. 没 is usually used to negate either 有 "have" or something in the past. E.g. 我没告诉你。 "I didn't tell you." 不 is used for everything else, i.e. 我不告诉你。 "I'm not telling you." (The interesting thing is that "have" also has a past aspect in English, e.g. "I have told you." But Mandarin doesn't use 有 as a general past marker, only the negation 没)
> I speak another Chinese dialect that also has this distinction, and I also can't tell you the rule there.
Which one? Is the rule the same as in Mandarin, i.e. can you produce correct Mandarin sentences despite not knowing the rule, relying just on intuition? I think Cantonese uses 冇 to negate 有.
More technically, 没 is the negative marker that applies to the verb 有, and 不 is the negative marker that applies to everything else. It isn't the 没 that marks a negative in the past as being past -- it is the (omitted) 有. That 有 is commonly not omitted in negative past sentences -- and it's also possible to use 有 to mark past time in positive-polarity sentences, though this is much rarer than the same marking in negative sentences.
There's a straightforward information-theoretic reason why 有 can be so commonly omitted -- it is the only thing that can ever follow 没, so actually realizing it doesn't add much. Everyone knows it's there.
> E.g. 我没告诉你。 "I didn't tell you."
This is the same sentence as 我没有告诉你, also fully idiomatic. The past sense is coming from the 有.
> But Mandarin doesn't use 有 as a general past marker, only the negation 没
This is plainly incorrect. 有 is used as a general past marker. It just isn't obligatory in positive-polarity sentences. Here are some things Chinese people have said to me:
你在中国 有看见过 美国没有的水果吗？("Have you seen any fruits in China that America doesn't have?")
我有吗 ("Did I?")
On the other hand, maybe that is a shortening of an originally obligatory two-part expression similar to Jespersen's cycle, famously observed in the appearance of "pas" and ongoing disappearance of "ne" in French "ne ... pas". https://en.wikipedia.org/wiki/Jespersen%27s_Cycle
As you can see, there's more than one way to negate something. Well it's hard for me to know if the rule is the same, given that I don't really know what the rule is in either! As per my previous comment I can tell you what sounds right, but I can't tell you why.
On the learning side, you also often get told rules that don't entirely make sense. For instance I'm told in a Mandarin class that there's a difference between 不 and 没 which is whether it's subjective or objective that something isn't true. But that's neither clear when saying something, nor clear in terms of examples I've been given. What's really weird is I speak another Chinese dialect that also has this distinction, and I also can't tell you the rule there.