Hi makenzi.exc,
You need to specify the TimeZone in toLocaleString method to formatting.
For India the TimeZone should be Asia/Kolkata.
Refer below example.
HTML
<html>
<head>
<meta charset="utf-8" />
<title></title>
<style type="text/css">
body { font-family: Arial; font-size: 10pt; }
</style>
</head>
<body>
<input type="button" value="Submit" onclick="IndianDateTime()" />
<script type="text/javascript">
function IndianDateTime() {
var dt = new Date();
alert(dt.toLocaleString("en-IN", { timeZone: 'Asia/Kolkata' }));
};
</script>
</body>
</html>
Demo
Screenshot

Downloads
Download Sample