I'm a native speaker, and I disagree with your grammar book, though I might be wrong. For one thing, I'm fairly confident you can use the past perfect tense:
"He had just arrived when suddenly gunshots were heard in the crowd."
Or the past continuous tense:
"He was just arriving as the gates were being opened to let in patrons."
I also say "I just ate there last week," and similar, which is past simple, and "I've just been talking to Alice," which is present perfect continuous.
Heck, you can even say, "I will have just landed when the call is scheduled to begin," which is future perfect.
If your question is pertaining to casual speech and writing, I'd say you are more than safe to use 'just' in any of these contexts. A grammarian may be able to give you a more technical answer.