Android で、Application#onTerminate() メソッドは実機端末では動作しないみたいです。

public void onTerminate ()

This method is for use in emulated process environments. It will never be called on a production Android device, where processes are removed by simply killing them; no user code (including this callback) is executed when doing so.

[引用元]：Application#onTerminate() | Android Developers

詳しくは下記の記事を参考に。

・baroqueworksdevの日記: Application#onTerminate()がコールされない

・La chiave a sviluppo del software.: Application#onTerminateは、実機では呼ばれない。