Two different things called a download
Downloading an application and downloading a film are separate actions. An application installs software on a device; an offline movie is a particular copy offered by the service playing it. Installing something with the Popcorn Time name does not automatically supply the film you want.
Here, you can browse in the browser and follow Watch now without installing a desktop program. This page does not contain an APK, executable installer or downloadable movie file. It is the place to find the right next step without guessing what a download button will provide.
Planning for a journey
Choose your film before leaving, open its viewing options for your country and check whether your chosen service supports offline viewing on that device and plan. Complete the download in that service, then test it before losing your connection. A film in My List is a reminder, not an offline copy.
Keep the choices, too
Your list can still be useful when planning the journey. Save several films of different lengths, then use list backup to keep a text copy of your choices. Subtitles and expiry rules for downloaded video belong to the service supplying the copy, so check those before travelling.