Disable initial automatic ajax call - DataTable server side paging

You could use the deferLoading parameter and set it to 0. This will delay the loading of data until a filter, sorting action or draw/reload Ajax happens programmatically.

function initTestTable(){
    myTable =  $('#testTable').dataTable({
    "processing": true,
    "serverSide": true,
    "deferLoading": 0, // here
    "ajax": {
        "url": "testTableData.html",
        "type": "GET",
    },
    "columns": [
        { "data": "code" },
        { "data": "description" }
    ]
 });
}

To trigger the Ajax when the button is clicked you can have something like the following in the handler:

function buttonClickHandler(event){
  $('#testTable').DataTable().draw();
}

See example below for demonstration.

$(document).ready(function() {
  // AJAX emulation for demonstration only
  $.mockjax({
      url: '/test/0',
      responseTime: 200,
      response: function(settings){
         this.responseText = {
            draw: settings.data.draw,
            data: [
              [ "Tiger Nixon", "System Architect", "Edinburgh", 61, "2011/04/25", "$320,800" ],
              [ "Tiger Nixon", "System Architect", "Edinburgh", 61, "2011/04/25", "$320,800" ],
              [ "Tiger Nixon", "System Architect", "Edinburgh", 61, "2011/04/25", "$320,800" ],
              [ "Tiger Nixon", "System Architect", "Edinburgh", 61, "2011/04/25", "$320,800" ],
              [ "Tiger Nixon", "System Architect", "Edinburgh", 61, "2011/04/25", "$320,800" ],
              [ "Tiger Nixon", "System Architect", "Edinburgh", 61, "2011/04/25", "$320,800" ],
              [ "Tiger Nixon", "System Architect", "Edinburgh", 61, "2011/04/25", "$320,800" ],
              [ "Tiger Nixon", "System Architect", "Edinburgh", 61, "2011/04/25", "$320,800" ],
              [ "Tiger Nixon", "System Architect", "Edinburgh", 61, "2011/04/25", "$320,800" ],
              [ "Tiger Nixon", "System Architect", "Edinburgh", 61, "2011/04/25", "$320,800" ]
            ],
            recordsTotal: 1000,
            recordsFiltered: 1000
         };
      }
  });

  $('#example').DataTable({    
    "processing": true,
    "serverSide": true,
    "deferLoading": 0,
    "ajax": {
        "url": "/test/0",
        "type": "GET"
    }    
  });
      
  $('#btn-reload').on('click', function(){
     $('#example').DataTable().draw()  
  });
});
<!DOCTYPE html>
<html>

<head>
<meta charset="ISO-8859-1">
<link href="//cdn.datatables.net/1.10.5/css/jquery.dataTables.min.css" rel="stylesheet"/> 
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.3/jquery.min.js"></script> 
<script src="//cdn.datatables.net/1.10.5/js/jquery.dataTables.min.js"></script>
<script src="http://vitalets.github.com/x-editable/assets/mockjax/jquery.mockjax.js"></script>
  
</head>
<body>
<p>
<button id="btn-reload">Reload</button>
</p>
<table id="example" class="display" cellspacing="0" width="100%">

<thead>
   <tr>
      <th>Name</th>
      <th>Position</th>
      <th>Office</th>
      <th>Age</th>
      <th>Start date</th>
      <th>Salary</th>
   </tr>
</thead>

<tfoot>
   <tr>
      <th>Name</th>
      <th>Position</th>
      <th>Office</th>
      <th>Age</th>
      <th>Start date</th>
      <th>Salary</th>
   </tr>
</tfoot>

<tbody>
</tbody>
</table>
</body>
</html>

I could do it with a workaround by passing an extra parameter with the URL to identify the event.

For example, for on load I initialized the data table with action="load" as query param and for other action like search, am passing action="search". With this I, at the back end, will be able to identify the call origin. If it is anything other than "load", I am pulling the data & passing (as the implementation is now). Otherwise (if "load") then I am passing empty data, which will show me "No Data Found" message as if it did not made the ajax call.

Here is my code - Table initialization:

function initTestTable(){
    myTable =  $('#testTable').dataTable({
    "processing": true,
    "serverSide": true,
    "ajax": {
        "url": "testTableData.html?action=load",
        "type": "GET",
    },
    "columns": [
        { "data": "code" },
        { "data": "description" }
    ]
 });
}

For events other than load (say button click):

    var newUrl = 'testTableData.html?action=search';
    myTable.api().ajax.url(newUrl).load();

This was the one I had to take up without modifications to table init that would cause errors.

Thank you @JSelser and @davidkonrad for all your suggestions :)