NOT A TEACHER
It is exactly as you are saying. "I just phoned him." would rarely (if ever) be uttered by a British person, but it is very common in AmE. "I have just phoned him." is used in AmE too. I think that it is widely known fact that AmE is a bit more flexible and less strict as far as English grammar is concerned. Btw. that is one of the reasons why I prefer it and try to use this variation of English.
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