Those are, unfortunately, not the correct rules, since, as you point out, they don't apply everywhere.
First, present perfect is not what's called a "tense" in grammar; real tenses modify verbs, like see/saw or look/looked -- they don't add auxiliary verbs. There are dozens of constructions (like Perfect, Passive, Progressive) that use auxiliary verbs stacked up, like
- We used to have to go get tested every week.
They can't all be called tenses.
Second, the constructions and tenses that a verb can appear in depend a great deal on the meaning of the verb. Some verbs are Stative and some are Active; some states are stable and some are changeable; some actions have endpoints and others don't; and so on.
Consequently there are four principal uses of the Perfect construction in the present tense, from McCawley 1971§
- (a) The Universal sense of the Perfect, used to indicate that a state of affairs prevailed throughout some interval stretching from the past into the present
• I've known Max since 1960.
This usage is common with statives like live (in a place) and with ongoing activities.
- (b) The Existential sense of the Perfect, used to indicate the existence of past events,
• I have read Principia Mathematica five times.
This usage occurs with active events or frequently changing states to signal whether (and how often) events have occurred.
- (c) The Stative/Resultative sense of the Perfect,
used to indicate that the direct effect of a past event still continues
• I can't come to your party tonight - I've caught the flu.
This usage is the one that licenses the equivalence of have got with have; if you have caught a cold, you still have it. This is often called "present relevance" in textbooks, but what it really means is that the event has not yet concluded, at least in its relation to the present.
- (d) The Hot News sense of the Perfect, used to report hot news
• Malcolm X has just been assassinated.
Finally, the Hot News sense is only applicable to punctual events in the recent past. Today, in 2022, we wouldn't say Malcolm X has been assassinated; we'd use the past tense. But we could say Nuclear fusion has been achieved because that was announced just today.
So, you have to know what the verb means and how it can fit into a Perfect construction; not everything can, and not all the same way. For instance, there's the famous Groucho Marx gag
- Thank you, ma'am. I've had a wonderful time. But this wasn't it.
The joke is that "I've had a wonderful time" is a common gracious leave-taking phrase, where the usage is Universal, while This wasn't it reinterprets the phrase literally as Existential ("at some time in the past I had a wonderful time"), and then denies that this was it. Compliment turned to insult, a Groucho specialty.
§ McCawley, James D. 1971. Tense and time reference in English. In C. Fillmore and T. Langendoen (eds.), *Studies in Linguistic Semantics*. New York: Holt, Rinehart and Winston, pp 96-113.