I using the latest version of library, but every time when I launch app on device with android 5+ I have a gap like on screen:
http://snag.gy/ugDqX.jpg
On device with Android 4.4 everything is fine:
http://snag.gy/yDSf3.jpg

I have the same issue. Here is an snippet.

activity_layout.xml

<?xml version="1.0" encoding="utf-8"?>
<android.support.design.widget.CoordinatorLayout
    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"
    android:background="@color/bg_light_grey">

    <include layout="@layout/toolbar"/>

    <RelativeLayout
        android:layout_width="match_parent"
        android:layout_height="match_parent"
        app:layout_behavior="@string/appbar_scrolling_view_behavior">

        <FrameLayout
            android:id="@+id/fragmentContainer"
            android:layout_width="match_parent"
            android:layout_height="match_parent" />

    </RelativeLayout>

</android.support.design.widget.CoordinatorLayout>

toolbar.xml

<?xml version="1.0" encoding="utf-8"?>
<android.support.design.widget.AppBarLayout
    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="wrap_content"
    android:fitsSystemWindows="true">

    <android.support.v7.widget.Toolbar
        android:id="@+id/toolbar"
        android:layout_width="match_parent"
        android:layout_height="?attr/actionBarSize"
        app:layout_scrollFlags="scroll|enterAlways"
        android:background="@color/primary"
        android:theme="@style/AppTheme.ActionBar"/>

</android.support.design.widget.AppBarLayout>

MainActivity.java

...
    private BottomBar mBottomBar;

@Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        getActivityComponent().inject(this);
        setContentView(R.layout.activity_layout);
        ButterKnife.bind(this);
        setupToolbar();
        setupBottomBar(savedInstanceState);
    }

    @Override
    protected void onSaveInstanceState(Bundle outState) {
        super.onSaveInstanceState(outState);

        // Necessary to restore the BottomBar's state, otherwise we would
        // lose the current tab on orientation change.
        mBottomBar.onSaveInstanceState(outState);
    }

    private void setupToolbar() {
        setSupportActionBar(mToolbar);
    }

    private void setupBottomBar(Bundle savedInstanceState) {
        mBottomBar = BottomBar.attach(this, savedInstanceState);
        mBottomBar.setItemsFromMenu(R.menu.bottombar, new OnMenuTabSelectedListener() {
            @Override
            public void onMenuItemSelected(int resId) {
                if (resId == R.id.bottomBarHome) {
                    // the user selected item number one
                }
            }
        });

        // Setting colors for different tabs when there's more than three of them.
        // You can set colors for tabs in three different ways as shown below.
        mBottomBar.mapColorForTab(0, ContextCompat.getColor(this, R.color.accent));
        mBottomBar.mapColorForTab(1, 0xFF5D4037);
        mBottomBar.mapColorForTab(2, "#7B1FA2");
        mBottomBar.mapColorForTab(3, "#FF5252");
    }

BTW, thanks of this awesome library. :)

Looking forward for new updates.

EDIT: With mBottomBar.noTopOffset(); doesn't work either, there is an overlap of the toolbar and the statusbar.

@roughike Nope, now it overlaps not only the statusbar (the toolbar) but the navigation bar as well (the bottombar). BTW, I'm testing in a Moto G 3rd Gen 6.0

Great! I made it to work just adding:
mBottomBar.useOnlyStatusBarTopOffset();
And I didn't have to change; android:fitsSystemWindows="true"
Thanks!

I found a new issue but I think is related. It doesn't work if we attach a recycleview. The toolbar doesn't completely disappear when we scroll, just the top half of it if mBottomBar.useOnlyStatusBarTopOffset(); is enabled.

On the other side if we use mBottomBar.noTopOffset(); it only shows the bottom half of the Toolbar without scroll. In this case when we scroll all the toolbar is correctly hided.

Thanks

@grocaDW mBottomBar.useOnlyStatusBarTopOffset(); works for me too ! Great, thank you