'The Indefinite Past does not tell you exactly when [something happened; e.g.,] at six o'clock this morning / three hours ago. [Those are] Incompatible with Present Perfect.'
Adverbials occuring with the Past Simple but precluding the Present Perfect: A WEEK AGO, EARLIER THIS YEAR, LAST MONDAY, THE OTHER DAY, YESTERDAY EVENING.
Adverbials which are most likely found in the Past Simple but can occur in an indefinite or iterative sense in the Present Perfect: AT FOUR O'CLOCK, IN THE MORNING, ON TUESDAY, THEN, SOON, NEXT, AFTER BREAKFAST. I've always done my HW in the evenings.
Adverbials which may accompany the Present Perfect but not the Past Simple include FOR THE PRESENT, FOR NOW, FOR THE TIME BEING.
Adverbials which are normally associated with the Present Perfect as opposed to the Past Simple, are SO FAR, UP TO NOW, HITHERTO, SINCE THURSDAY, SINCE I MET HER and LATELY & LATTERLY (recent indefinite past)
The group of adverbials which combine with either Present Perfect or Past Simple is interesting in so far as it indicates cases where the two tenses are interchangeable as well as instances where the actual meaning depends on the tense.
ALWAYS, EVER and NEVER can be used either with the Present Perfect or Past Simple: I've always said / I always said. He's always been a liar / He always was a liar.
NOW & ONCE: Now I've nearly finished my tea. Now it was nearly dark (for "then). I've visited Toledo once / Once I was innocent (at one time). Meaning change.
ALREADY, STILL, YET & BEFORE relate to point of orientation "now" when used with the Present Perfect and "then" when used with the Past Simple.
I've already finished it (as early as now) / I was already very tired (as early as then). Syntax and semantics - English verb tenses and their uses