Solution number 1 :
You Have to do like following to reach "near" to your functionality,
Wrap the adapter of your ListView
Like following :
  protected void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    // Create an Adapter for your content
    String[] content = new String[20];
    for (int i=0;i<20;i++) content[i] = "Row "+(i+1);
    ArrayAdapter<String> stringAdapter = new ArrayAdapter<String>(
        this,
        R.layout.row_bg,
        R.id.text,
        new ArrayList<String>(Arrays.asList(content))
    );
   // Wrap your content in a SwipeActionAdapter
   mAdapter = new SwipeActionAdapter(stringAdapter);
   // Pass a reference of your ListView to the SwipeActionAdapter
   mAdapter.setListView(getListView());
   // Set the SwipeActionAdapter as the Adapter for your ListView
   setListAdapter(mAdapter);
  }
Create a background layout for each swipe direction
Like Following:
  protected void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
   // Create an Adapter for your content
   String[] content = new String[20];
   for (int i=0;i<20;i++) content[i] = "Row "+(i+1);
   ArrayAdapter<String> stringAdapter = new ArrayAdapter<String>(
        this,
        R.layout.row_bg,
        R.id.text,
        new ArrayList<String>(Arrays.asList(content))
   );
   // Wrap your content in a SwipeActionAdapter
   mAdapter = new SwipeActionAdapter(stringAdapter);
   // Pass a reference of your ListView to the SwipeActionAdapter
   mAdapter.setListView(getListView());
   // Set the SwipeActionAdapter as the Adapter for your ListView
   setListAdapter(mAdapter);
   // Set backgrounds for the swipe directions
    mAdapter.addBackground(SwipeDirections.DIRECTION_FAR_LEFT,R.layout.row_bg_left_far)
          .addBackground(SwipeDirections.DIRECTION_NORMAL_LEFT,R.layout.row_bg_left)
         .addBackground(SwipeDirections.DIRECTION_FAR_RIGHT,R.layout.row_bg_right_far)
        .addBackground(SwipeDirections.DIRECTION_NORMAL_RIGHT,R.layout.row_bg_right);
}
You got both libraries and Example from the here :
https://github.com/wdullaer/SwipeActionAdapter
This will not exact like you want, but i hope this will help you so much to fulfilled your functionality.
Solution number 2 : 
Solution 2 is about  Changing some code in your Used code : http://www.tutecentral.com/android-swipe-listview/ 
i had try your code from the link http://www.tutecentral.com/android-swipe-listview/  and changing some code and successfully solve your problem(your confusion) about onOpened(..)  method ( called left to right and vice versa )  
First change :  
- custom_row.xml layout file has three button swipe_button1 to 3 ,
remove middle of them. 
- Copy paste following code for remain two button : - <Button
    android:id="@+id/swipe_button1"
    android:layout_width="48dp"
    android:layout_height="48dp"
    android:layout_alignParentLeft="true"
    android:layout_alignParentTop="true"
    android:background="@drawable/your_accept_image" />
<Button
    android:id="@+id/swipe_button3"
    style="@style/MyListButtonAction"
    android:layout_width="48dp"
    android:layout_height="48dp"
    android:layout_alignParentRight="true"
    android:layout_alignParentTop="true"
    android:background="@drawable/your_reject_image" />
 
Remains code same for this layout.
Second change :
So now your accept and reject and list code is ready , now discuss about onOpened(..) method.
Confusion solution 1- You told , your onOpend(...) method called same both left to right and vice-verse 
-> just to change following :
public void onOpened(int position, boolean toRight) {
            if(toRight)
            {
                //  for left to right your api calling here
                swipelistview.closeAnimate(position);
            }
            else
            {
                // for right to left your api calling here
                swipelistview.closeAnimate(position);
            }
        }
Confusion solution 2 when i take finger up it will must display entire listview or listview sides should retain it corners so its not working 
-> i already answered it in above
called swipelistview.closeAnimate(position); in both if else, it hide left accept and right reject image when your your swipe left and right over.
So final code is following :
Entire cutom_row.xml layout 
 <?xml version="1.0" encoding="utf-8"?>
 <FrameLayout xmlns:android="http://schemas.android.com/apk/res/android"
     android:layout_width="fill_parent"
     android:layout_height="fill_parent" >
  <RelativeLayout
    android:id="@+id/back"
    android:layout_width="match_parent"
    android:layout_height="wrap_content"
    android:tag="back" >
    <Button
        android:id="@+id/swipe_button1"
        android:layout_width="48dp"
        android:layout_height="48dp"
        android:layout_alignParentLeft="true"
        android:layout_alignParentTop="true"
        android:background="@drawable/accept_image" />
    <Button
        android:id="@+id/swipe_button3"
        style="@style/MyListButtonAction"
        android:layout_width="48dp"
        android:layout_height="48dp"
        android:layout_alignParentRight="true"
        android:layout_alignParentTop="true"
        android:background="@drawable/reject_image" />
</RelativeLayout>
<RelativeLayout
    android:id="@+id/front"
    style="@style/MyListFrontContent"
    android:orientation="vertical"
    android:tag="front" >
    <ImageView
        android:id="@+id/example_image"
        style="@style/MyListImage" />
    <TextView
        android:id="@+id/example_itemname"
        style="@style/MyListTitle"
        android:layout_width="fill_parent"
        android:layout_height="wrap_content"
        android:layout_toRightOf="@id/example_image" />
  </RelativeLayout>
</FrameLayout>
Entire MainActivity.java
public class MainActivity extends Activity {
SwipeListView swipelistview;
ItemAdapter adapter;
List<ItemRow> itemData;
@Override
protected void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    setContentView(R.layout.activity_main);
    swipelistview=(SwipeListView)findViewById(R.id.example_swipe_lv_list); 
    itemData=new ArrayList<ItemRow>();
    adapter=new ItemAdapter(this,R.layout.custom_row,itemData);
    swipelistview.setSwipeListViewListener(new BaseSwipeListViewListener() {
        @Override
        public void onOpened(int position, boolean toRight) {
            if(toRight)
            {
                //  for left to right your api calling here
                swipelistview.closeAnimate(position);
            }
            else
            {
                // for right to left your api calling here
                swipelistview.closeAnimate(position);
            }
        }
        @Override
        public void onClosed(int position, boolean fromRight) {
            // close list slide
        }
        @Override
        public void onListChanged() {
        }
        @Override
        public void onMove(int position, float x) {
        }
        @Override
        public void onStartOpen(int position, int action, boolean right) {
            Log.d("swipe", String.format("onStartOpen %d - action %d", position, action));
        }
        @Override
        public void onStartClose(int position, boolean right) {
            Log.d("swipe", String.format("onStartClose %d", position));
        }
        @Override
        public void onClickFrontView(int position) {
            Log.d("swipe", String.format("onClickFrontView %d", position));
        }
        @Override
        public void onClickBackView(int position) {
            Log.d("swipe", String.format("onClickBackView %d", position));
            swipelistview.closeAnimate(position);//when you touch back view it will close
        }
        @Override
        public void onDismiss(int[] reverseSortedPositions) {
        }
    });
    //These are the swipe listview settings. you can change these
    //setting as your requirement 
    swipelistview.setSwipeMode(SwipeListView.SWIPE_MODE_BOTH); // there are five swiping modes
    //    swipelistview.setSwipeActionLeft(SwipeListView.SWIPE_ACTION_DISMISS); //there are four swipe actions 
    swipelistview.setSwipeActionRight(SwipeListView.SWIPE_ACTION_REVEAL);
    swipelistview.setOffsetLeft(convertDpToPixel(0f)); // left side offset
    swipelistview.setOffsetRight(convertDpToPixel(80f)); // right side offset
    swipelistview.setAnimationTime(500); // Animation time
    swipelistview.setSwipeOpenOnLongPress(true); // enable or disable SwipeOpenOnLongPress
    swipelistview.setAdapter(adapter);
    for(int i=0;i<10;i++)
    {
        itemData.add(new ItemRow("Swipe Item"+ i,getResources().getDrawable(R.drawable.ic_launcher) ));
    }
    adapter.notifyDataSetChanged();
}
public int convertDpToPixel(float dp) {
    DisplayMetrics metrics = getResources().getDisplayMetrics();
    float px = dp * (metrics.densityDpi / 160f);
    return (int) px;
}
@Override
public boolean onCreateOptionsMenu(Menu menu) {
    // Inflate the menu; this adds items to the action bar if it is present.
    getMenuInflater().inflate(R.menu.main, menu);
    return true;
  }
 }
Other code and library remains same, It helpful to you and other also, So enjoy.