The app works for 1) arXiv papers 2) any url of a paper obtainable from the address bar of your phone.
If you copy-paste, or copy and use the clipboard button, it will try to identify the arXiv identifier from the url, and then show you the title + abstract. Then you have to download the PDF, preview the transformed copy (copy stays in the cloud for 24h), and finally request a fully reflowed copy. The reflow is limited to about 30s via AWS Lambda, so this is not for dissertations -- this is for 2-20 page papers you can reasonably read on your phone. Nevertheless, there is a progress bar at the top of the screen to show you it's working, at that stage. These steps are pretty much reproduced in the app store images.
For a non-arXiv link, the only difference is that there is no abstract. But note, the link can't just be to the journal page, you've got to get a PDF mime-type when it's requested.
There are some things I should change, but it's very useful to me, and I just verified it works for both arXiv and non-arXiv. If it's not working for you, I would suggest deleting and reinstalling (sorry!).