On some devices, the built-in "Web View" component we use to render the Bible text cannot handle both the "textured background" on the entire page and the colored background on text. It is actually rendering the colored background behind the verse text, but it is under the textured background image so you can't see it.
On these devices, you need to disable "textured backgrounds" in order to see highlighted passages. You can do that in the Settings menu.
As we've implied here, this is a device issue, not a PocketBible issue. You may find that the next Android device you buy, especially if it is from a different manufacturer, will work fine. Or the next Android OS update will fix it.