Fetch data using AJAX and Codeigniter?

Your code hints at other relevant code that is not shown. I'm taking what you show as all that needs to be known. Here's what I see based on that premise.

First, the view. Add an id to the table. It makes JQuery selectors so much easier. The JavaScript is in this file which is "users/allusersusingajax.php".

<div class="userdataajax table-responsive">
    <table id='user-table' class=" table table-responsive table-bordered">
        <tr>
            <th>#</th>
            <th>name</th>
            <th>image</th>
            <th> full name</th>
            <th>email</th>
            <th>usertype</th>
            <th>status</th>
            <th>reg date</th>
            <th>reg time</th>
            <th>delete</th>
            <th>edit</th>
            <th>Activate</th>
            <th>disactivate</th>
        </tr>
    </table>
</div>

<script>
    $(document).ready(function () {

        function FetchAllViaAjax() {
            $.ajax({
                url: '<?= base_url("users/get_all_users") ?>',
                method: "post",
                dataType: 'html',
                success: function (data) {
                    var table = $("#user-table");
                    table.not("table tr:first").remove();//your code makes it unclear why you need this 
                    table.append(data);
                }
            });

            FetchAllViaAjax();
        }
    });

</script>

The controller needs two methods. One to show the table another to get the rows. This is the file Users.php

//show the page which includes the basic <table> and header row
public function indexajax()
{
    // The code and question text give no reason for this conditional test 
    // So I'm removing it
    //if($this->input->post("action") == 'FetchAllUserUingAjax')
    //{
    $data['pagetitle'] = "-->All Users Using Ajax<--";
    $this->load->view("template/admin/header", $data);
    $this->load->view("users/allusersusingajax");
    $this->load->view("template/admin/footer");
    //}
}

//respond to ajax request
public function get_all_users()
{
    $this->load->model("usersmodel");
    $allu = $this->usersmodel->ShowAllUsers("users");

    $out = ''; //if the model returned an empty array we still have a string to echo
    //using PHP's output buffer to simplify creating a big string of html
    ob_start(); //start output buffering
    foreach($allu as $a):
        ?>
        <tr><td><?= $a->id; ?></td><td><?= $a->username; ?></td></tr>
        <?php
    endforeach;
    $out .= ob_get_clean(); //append the output buffer to the $out string
    echo $out;
}

Read about PHP's Output Control Functions

I'd first update my model to return an array:

return $sql->result_array();

Then in your controller, you don't need to load a view:

 public function indexajax()
 {
    if($this->input->post("action")=='FetchAllUserUingAjax')
    {
        //set content type
        header("Content-type: application/json");

        $this->load->model("usersmodel");

        echo json_encode(
            $this->usersmodel->ShowAllUsers(); //this method doesn't expect an argument, no need to pass one
        );

    }
  }

Then in your ajax callback:

success: function(resp){
   $.each(resp, function(k,v){
      console.log(v); 
   });  
}