Getting click on item to open closest relevant element (popup) with jQuery

You are facing this issue because all your popup container divisions have the same id and all the popup open can close buttons are targeting the same id. Change your code as follow:

<td>
    <h4>Alert #1</h4>
    <a href="#" class="open-alert-popup" data-id="popup_alerts_1" data-animation="flipAlertsRight">Open Button</a>
      <!- below div is hidden till above link is clicked ->     
      <div id="popup_alerts_1" class="alert-popup" style="display: none;">
         <div class="alert-popup-overlay"></div>
         <div class="alert-popup-content">
            <a href="#" class="close-alert-popup" data-id="popup_alerts_1" data-animation="flipAlertsRight">Close Button</a>
                <!- some popup content here ->
         </div>
      </div>
</td>
<td>
    <h4>Alert #2</h4>
    <a href="#" class="open-alert-popup" data-id="popup_alerts_2" data-animation="flipAlertsRight">Open Button</a>
      <!- below div is hidden till above link is clicked ->     
      <div id="popup_alerts_2" class="alert-popup" style="display: none;">
         <div class="alert-popup-overlay"></div>
         <div class="alert-popup-content">
            <a href="#" class="close-alert-popup" data-id="popup_alerts_2" data-animation="flipAlertsRight">Close Button</a>
                <!- some popup content here ->
         </div>
      </div>
</td>
<td>
    <h4>Alert #3</h4>
    <a href="#" class="open-alert-popup" data-id="popup_alerts_3" data-animation="flipAlertsRight">Open Button</a>
      <!- below div is hidden till above link is clicked ->     
      <div id="popup_alerts_3" class="alert-popup" style="display: none;">
         <div class="alert-popup-overlay"></div>
         <div class="alert-popup-content">
            <a href="#" class="close-alert-popup" data-id="popup_alerts_3" data-animation="flipAlertsRight">Close Button</a>
                <!- some popup content here ->
         </div>
      </div>
</td>

jQuery operates on first identified elements basis when it comes to id attributes because ids are supposed to be unique for each element on the page. You will see that changing the data-id attribute and id attribute resolves all your problem and you can make it dynamic if the content that you are showing is coming from a loop.