This seems to be some kind of bug~conflict in particular set-ups as @Daniel did not have any problems in Chrome or Safari. But I did under certain circumstances.
Note: All below use OSX 10.11.6; Hype 3.6.3 (584).
Chrome (60.0.3112.90), Firefox (54.0.1), Opera (44.0.2510.1218) do work properly for me.
Safari 10.1.1 - I have the same issue as You - the animated page does not scroll properly. But the following (2) options work in my set-up.
Option 1: Checking the "Position with CSS left/top" in Hype's "Document Inspector" Safari 10.1.1 does work. Note: It scrolls but scrollbars are not shown in my rendering.
Option 2: Uncheck "Use WebKit graphics acceleration" (shown "checked" in Fig. 1 below).
Note: The scrollbars are shown in my rendering. You do not need to also use "Option 1".
Fig.1 - "Document Inspector" screenshot crop
So this is where it gets interesting: DocumentsBrowserTest_JHS.hype.zip (81.2 KB)
Using your original file... I re-did your animated scene so it was showing in the Scene to start (not below the Scene boundary as in your version). It worked in Safari. Neither "Option 1" or "Option 2" was used. All settings in the "Document Inspector" the same as your original.