I'm having the same problem, i solved the scrolling but putting toolbar and the tabs inside the app bar and wrap it and the viewpager with a coordinatorlayout.
Also in the layout of my recycle view(to be inflated) i add the layout_behavior. It works but the problem is everything is over each other.
This is my main page
<android.support.design.widget.CoordinatorLayout
android:layout_width="match_parent"
android:layout_height="match_parent"
android:layout_above="@+id/music_foot"
>
<android.support.v4.view.ViewPager
android:layout_width="match_parent"
android:layout_height="match_parent"
android:id="@+id/view_pager"
/>
<view
android:layout_width="match_parent"
android:layout_height="wrap_content"
class="android.support.design.widget.AppBarLayout"
android:id="@+id/appBar"
>
<android.support.v7.widget.Toolbar
android:layout_width="match_parent"
android:layout_height="56dp"
android:background="#1e88e5"
android:id="@+id/toolbar"
app:layout_scrollFlags="scroll|enterAlways"
></android.support.v7.widget.Toolbar>
<view
android:layout_width="match_parent"
android:layout_height="56dp"
class="com.astuetz.PagerSlidingTabStrip"
android:id="@+id/pager_tabs"
android:layout_below="@+id/appBar"
android:layout_alignParentLeft="true"
android:layout_alignParentStart="true" />
</view>
and this is my layout for the adapter
<android.support.v7.widget.RecyclerView
xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:app="http://schemas.android.com/apk/res-auto"
android:layout_width="match_parent"
android:layout_height="match_parent"
app:layout_behavior="@string/appbar_scrolling_view_behavior"
android:id="@+id/recycleView" />
If I get it to work better ill tell you.