Your PL/SQL code should be like this:

Declare
v_cntr number;
v_count number;
v_pop_up number;
begin
   update employee
   enddate = to_date(’08/18/2020′,’mm/dd/yyyy’)
    where emp_id = :P45_POP_UP;

   If sql%rowcount > 0 Then
      htp.prn(‘SUCCESS’);
   Else
      htp.prn(‘Error while updating table.’);
   End If;
End;

I am assuming the page item P45_POP_UP is the employee id or if it is not then I think you should pass employee id page item to it.

In the 2nd step, in which you are calling the Ajax process using the JavaScript code, put that JS code between the if condition, as shown in the below example:

apex.message.confirm( "Confirm to update table B?", function( okPressed ) { 
if( okPressed ) {
// add your JavaScript code here
} 
});

Or if this part is already working, then you can refer to the following post in which I have given an example to call the Ajax process using JavaScript.

Calling Ajax Process from JavaScript in Oracle Apex.

That example is related to the validation, you just ignore that part and use the PL/SQL code to update your table.

Let me know if any questions.

You can do one more thing.

Hide the close (X) button of the dialog so that the user has to click on the Cancel/Close button to close the dialog.

Add the following CSS to the parent page. In the page settings > Inline CSS:

body .ui-dialog .ui-dialog-titlebar-close {display: none;}

Note: Do not add the above CSS to the dialog page.

Even I used this approach sometimes.