Once you drag them down to your party, located at the bottom of the screen, you should see a greenish continue arrow display along the right side of the screen. Tap that to continue.
Sorry to necro this thread, but I just installed the android app today on my Nexus 5x and I'm getting the same issue, no way to continue from the party screen after completing the tutorial.
android 7.1.2
PFID-2318F707E1DD0EEB