Use of "would have" unclear

Consider the following two sentences:

For now, we cannot be sure how the machine worked back then. But once it existed, people would immediately have used it.

Sentences like these, where the first is "regular" and the second uses "would have", are used again and again over several paragraphs to lay out the history of the machine and what the author thinks is true about that history. From context, it seems clear that the author thinks the machine really did exist, and that people really did use it immediately once it existed.

Why does the author say "people would immediately have used it" instead of just "people immediately used it"? Is this an idiomatic way of allowing for the possibility that he might be wrong, or is it something else? (Non-native speaker here.)

To answer your question specifically: Why does the author say "people would immediately have used it" instead of just "people immediately used it"?

My opinion is it's either poor command of English or careless writing.

It is puzzling just what the author of the sentences is actually trying to convey. Let me address the first sentence. It should simply read:

We cannot be sure how the machine worked back then.

As for the second sentence, the author likely meant one of the these two versions:

But had it existed, people would immediately have used it.

OR

But once it existed, people immediately used it.

This brings me to the end result:

We cannot be sure how the machine worked back then. But once it existed, people immediately used it.

If you would like to add some stylistic flair to it, it becomes:

We cannot be sure how the machine worked back then, but once it came into existence, people immediately started using it.