This method appears to follow these rules:
 - if $localName names a sibling node, the cursor is moved to that node;
 - if $localName names an ancestor node, the cursor is moved to the end of that node;
 - if $localName names a node that is a sibling of any of the current node's ancestors, the cursor is moved to that node;
 - otherwise the cursor is moved outside the document.
Note especially that this method never moves the cursor to child nodes.
For example, given this XML document
<?xml version="1.0" encoding="UTF-8"?>
<root id="root" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
  <aaa id="1">
    <bbb id="1.1"></bbb>
    <bbb id="1.2"></bbb>
  </aaa>
  <ccc id="2" />
  <aaa id="3">
    <ddd id="3.1">
      <aaa id="3.1.1"></aaa>
    </ddd>
    <aaa id="3.2"></aaa>
  </aaa>
  <aaa id="4">
    <eee id="4.1"></eee>
  </aaa>
</root>
going from <root id="root"> to "bbb" places the cursor outside the document;
going from <aaa id="1"> to "bbb" places the cursor outside the document;
going from <aaa id="1"> to "aaa" places the cursor on <aaa id="3">;
going from <bbb id="1.1"> to "bbb" places the cursor on <bbb id="1.2">;
going from <bbb id="1.2"> to "bbb" places the cursor outside the document;
going from <bbb id="1.1"> to "ddd" places the cursor outside the document;
going from <bbb id="1.1"> to "aaa" places the cursor on </aaa>;
going from <bbb id="1.1"> to "ccc" places the cursor on <ccc id="2">;
going from <bbb id="1.1"> to "nonsuch" places the cursor outside the document;
going from <bbb id="1.1"> to "root" places the cursor on </root>;
going from <ddd id="3.1"> to "aaa" places the cursor on <aaa id="3.2">;
going from <ddd id="3.1"> to "eee" places the cursor outside the document;
Try it yourself:
<?php
$document = <<<XML
<?xml version="1.0" encoding="UTF-8"?>
<root id="root" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
  <aaa id="1">
    <bbb id="1.1"></bbb>
    <bbb id="1.2"></bbb>
  </aaa>
  <ccc id="2" />
  <aaa id="3">
    <ddd id="3.1">
      <aaa id="3.1.1"></aaa>
    </ddd>
    <aaa id="3.2"></aaa>
  </aaa>
  <aaa id="4">
    <eee id="4.1"></eee>
  </aaa>
</root>
XML;
$filename = "/tmp/xmlreader.php.xml";
file_put_contents($filename, $document);
echo "given this XML document\n\n$document\n\n";
showNext("root", "bbb");
showNext("1", "bbb");
showNext("1", "aaa");
showNext("1.1", "bbb");
showNext("1.2", "bbb");
showNext("1.1", "ddd");
showNext("1.1", "aaa");
showNext("1.1", "ccc");
showNext("1.1", "nonsuch");
showNext("1.1", "root");
showNext("3.1", "aaa");
showNext("3.1", "eee");
function showNext($from, $to) {
  global $filename;
  $xml = new \XmlReader();
  $xml->open("file://$filename");
  while ($xml->read()) {
    if ($xml->nodeType === \XmlReader::ELEMENT) {
      if ($xml->getAttribute("id") == $from) {
        echo "going from <$xml->name id=\"$from\">";
        break;
      }
    }
  }
  $xml->next($to);
  $destination = "";
  if($xml->nodeType === \XmlReader::NONE) {
    if(!$xml->read()) {
      $destination = "outside the document";
    }
  }
  if(!$destination) {
    if ($xml->nodeType === \XmlReader::END_ELEMENT) {
      $destination = "on </$xml->name>";
    } else if ($xml->nodeType === \XmlReader::ELEMENT) {
      $destination = "on <$xml->name id=\"" . $xml->getAttribute("id") . "\">";
    }
  }
  echo " to \"$to\" places the cursor $destination;\n";
  $xml->close();
}
?>