Only having had one call with Branch.io, I am not terribly familiar with its architecture, however, I believe it depends upon your app having its own URL scheme such as twitter:// or fb://.
Luckily, there is a cordova plugin for this. It sounds like Branch is doing a GET on that link, and not receiving anything back, so it's redirecting you to your app's Play Store URL.
If you already have this installed, I would recommend testing the plugin alone to make sure you have it configured correctly (try testing your own generated link). If it is still not working, see if Branch has this app URL configured correctly.
If that still fails, I would contact Branch about some cordova example code and troubleshooting options: I know they specifically mentioned it when I talked to them.