When you download the original app from Play Store, it downloads an obb file, which contains firmware files of your drone and controller, during installation. However if you install an apk file outside Play Store, the app will download the obb file from somewhere in the initial startup, and Parrot used the word "synchronization" for this progress.
651obb.zip
This is the obb file. Download and unzip this on your phone's sdcard root directory.