At least for me, when I'm adding tags on mobile, I have to click a "Go" button at the bottom right of my virtual keyboard to make it add the tag. In that case, the tag will receive a blue background to indicate it's active and I can type another. If I just click away from the tag, somewhere else on the page, it will instead disappear. Of course, you will need to save the changes to the chapter as well.
Hopefully that helps, not sure if it's the full issue you're having.