I agree that it's a rather mysterious statement. This is my own interpretation, though it may be wrong:
Suppose MissX works in an office. Her manager, MrZ, gives her a report to read.
Next day, MrZ says to MissX: "So, what did you think of that report?"
"I thought it was very interesting," says MissX.
"Interesting?" says MrZ. "Are you sure you've read it?"
"Of course I've read it!" says MissX, indignantly. "In fact, I've read it very carefully indeed!"
The underlined parts are examples of the present perfect. The present perfect here denotes an event in the recent past which has relevance to the present moment.
In the last example, it would be unidiomatic to say "In fact, I've read it at 6 o'clock this morning!" Instead, you would have to use the simple past, if you wanted to state the specific time: "In fact, I read it at 6 o'clock this morning".
This is presumably what your author means, when he says that you may not mention a specific time in conjunction with the present perfect.
However, the speaker may well have a specific time in mind: the present perfect doesn't necessaily denote "vagueness about time". In the dialogue above, for instance, MissX may well be thinking of the specific time when she read the report, even though she doesn't mention it.
As for how you know whether the speaker has a specific time in mind: with the present perfect, you don't need to know the specific time. In other words, the present perfect is usually not used in contexts where it's necessary to state a specific time.
(But I may have entirely misunderstood your author's intentions: it's quite possible that another member understands it better than I do, or is familiar with the text in question. So hang on for other answers!)
All the best,