I think I figured out what the problem is :
If before saving my project (or simply closing Scrivener) I move the focus to another document in the binder, then the initial document as it’s displayed range right upon reopening the project.
In other words, it seems that for some reason, Scrivener doesn’t “memorize” the very last scroll position when saving a project. (It rather keeps going back over and over to the last one it has. So, even if you tweaked a document, and even a lot, as long as it is the last document you had displayed, the displayed range will go back to what it was before doing so. Might even be to what it was a couple sessions ago, if you pretty much end up having worked only on that specific document, or ended all those sessions with this specific document active.)