Bugs... or no bugs, but surely look like bugs..

Here is my *guess* (its a bit hard to see from the video). I think you are not using the "clipping mask" feature of Character Animator, but instead using white rectangles to hide other parts of the images. The order of the layers in the Illustrator file controls what is drawn on top of what. As soon as you start moving things around, those white rectangles probably move as well. That means and writing lower in the Illustrator file (more towards the bottom of the list) will be hidden if the white rectangles overlap the writing.

There is nothing wrong with this approach, but it would explain why the writing is being clipped off mid word. There is a white rectangle above in in the layer view, so the white rectangle is in front of the second half of the writing.

If this is correct, one approach is to move all the arrows and writing to the top of the screen - just drag them higher. No need to change the depth of anything, just have them drawn on top of any rectangles etc.

Regarding rig vs scene mode, normally "rig" mode is used to create a "puppet" (normally a character that walks around a scene etc). In your case, you have a mega puppet with everything in the same file. When you put writing in a separate AI file and load it, it creates a new puppet. If you drag the puppet into an existing puppet in rig mode, you are using a feature calls "shared puppets" where you can build a mega puppet out of smaller puppets. There is nothing wrong with doing this, but it does make the puppet more complicated. So yes, dragging puppets into the rig panel expands a current puppet.

For character puppets, you normally do one per character (could be one per device for you), then you (as you said) drag them into a scene. The one that appears higher in the scene timeline will be shown in front of other ones. E.g. if you load up writing in a separate file, then put it at the bottom of the timeline panel (the scene), it might still get clipped because it is behind the white artwork of the puppets above it. If you put it first, then it will appear on top. So when you drag writing puppets into the scene, make sure you put them before the device artwork, or else you might get the same problem of things hidden by white rectangles.

One way to test this theory is in the scene window there is a "mesh" icon at the bottom. It will draw yellow outline and triangles all over the puppet artwork (including the white rectangles). This might give you an idea where rectangles are.

Note: There have been bugs in Ch before, and will be in the future as well! The above is my guess as cropping writing seems like a strange bug (because its so simple). The fact that the writing was at the very bottom of the page (so will be behind all the other artwork in your file) is why I am suspicious that is the problem. Because you move things around during animation to show things moving etc, that might be why it looks good in the AI file, but has gone funny in CH record mode. Just a guess! 😉