The only way to get text selection from a WebView is based on javascript. This is not specific to the action mode, this is how WebView text selection is supposed to be retrieved according to WebView developers' point of view. They deliberately decided to not provide an API to access text selection from Java.
The solution comprise 2 approaches.
With Android API >= 19 you can use evaluateJavascript:
webview.evaluateJavascript("(function(){return window.getSelection().toString()})()",
new ValueCallback<String>()
{
    @Override
    public void onReceiveValue(String value)
    {
        Log.v(TAG, "SELECTION:" + value);
    }
});
On older builds your only resort is a custom javascript interface with a single method accepting String, which you should call via webview.loadUrl passing the same thing:
webview.loadUrl("javascript:js.callback(window.getSelection().toString())");
where js is the attached javascript interface:
webview.getSettings().setJavaScriptEnabled(true);
webview.addJavascriptInterface(new WebAppInterface(), "js");
and
public class WebAppInterface
{
    @JavascriptInterface
    public void callback(String value)
    {
        Log.v(TAG, "SELECTION:" + value);
    }
}
Answer from Here
UPDATE: 
For modifying and copy data (as your comment), Store the selected value in a member variable like "Seleted_Value" and when on clicking copy button (which is handling action mode - search about custom action mode) modify the "Selected_Value" variable and copy to clipboard using :
ClipboardManager clipboard = (ClipboardManager)
        getSystemService(Context.CLIPBOARD_SERVICE);
ClipData clip = ClipData.newPlainText("simple text",Selected_Value); 
clipboard.setPrimaryClip(clip);
Details here :