This function should be displaying both modified and published dates only if they differ.
if ( get_the_time( 'U' ) !== get_the_modified_time( 'U' ) ) {
$time_string = '<time class="entry-date published" datetime="%1$s">%2$s</time><time class="updated" datetime="%3$s">%4$s</time>';
}
Dates are compared using timestamps and if they don’t match the string format is set to two <time>
tags otherwise it’s just published date.