I can duplicate this in the latest github master. For others: here's a complete file suitable for testing.
Code:
<?xml version="1.0" encoding="utf-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1//EN"
"http://www.w3.org/TR/xhtml11/DTD/xhtml11.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<title></title>
</head>
<body>
<div class="whatever">
<h1> chapter 1</h1>
<hr class="sigil_split_marker" />
<h1> chapter 2</h1>
</div>
</body>
</html>
Split at Cursor (cursor placed before the hr or the 2nd h1) preserves the containing div in the newly created file. When using Split at Markers the containing div is NOT preserved in the newly created file.