Google Sheets – How to Timestamp New Added Cells in Live Spreadsheet

The code below insert timestamp in google sheet by editing another column.
However, there an issue which I have no idea how to solve. When I add new row manually, it successfully adds timestamp, BUT I have an html form in my website which sends data to this sheet and even-though new row is added, google don't create a timestamp !!!
It's a bit weird since conceptually when a new row is added, means an edit in cell, and google must add timestamp. I would be so grateful if someone help me to solve this issue.
Thanks

function onEdit(event)
{ 
  var timezone = "GMT+8:30";
  var timestamp_format = "yyyy-MM-dd HH:mm:ss"; // Timestamp Format. 
  var updateColName = "date";
  var timeStampColName = "Date Sent";
  var sheet = event.source.getSheetByName('Attendance'); //Name of the sheet where you want to run this script.


  var actRng = event.source.getActiveRange();
  var editColumn = actRng.getColumn();
  var index = actRng.getRowIndex();
  var headers = sheet.getRange(1, 1, 1, sheet.getLastColumn()).getValues();
  var dateCol = headers[0].indexOf(timeStampColName);
  var updateCol = headers[0].indexOf(updateColName); updateCol = updateCol+1;
  if (dateCol > -1 && index > 1 && editColumn == updateCol) { // only timestamp if 'Last Updated' header exists, but not in the header row itself!
    var cell = sheet.getRange(index, dateCol + 1);
    var date = Utilities.formatDate(new Date(), timezone, timestamp_format);
    cell.setValue(date);
  }
}