This is a very old "issue", which has existed since essentially forever, and it affects all of the available scrollModes. However, in the recently added Page-mode it's particularily noticeable since we use a *simulated* scroll direction there.
When deciding what page(s) to pre-render, we only consider the current scroll direction. This works well in most cases, but can break down at the start/end of the document by trying to pre-render a page *outside* of the existing ones. To improve this, we'll thus *force* the scroll direction at the start/end of the document.
*Steps to reproduce:*
0. Open the viewer, e.g. https://mozilla.github.io/pdf.js/web/viewer.html
1. Enable vertical scrolling.
2. Press the <kbd>End</kbd> key.
3. Open the devtools and, using the DOM Inspector, notice how page 13 is *not* being pre-rendered.