The values for the times in the Yesterday/Today min/max temperatures are all from WCTtags.php and reflect data in WeatherCat.
from your WCTtags.php?sce=dump shows
$WX['STAT:TEMPERATURE:MAX:TODAY'] = '62.0'; // Highest temperature today
$WX['STAT:TEMPERATURE:MAX:TODAY:TIME'] = '17:06:00'; // Time of highest temperature today
$WX['STAT:TEMPERATURE:MAX:YESTERDAY'] = '60.9'; // Highest temperature yesterday
$WX['STAT:TEMPERATURE:MAX:YESTERDAY:TIME'] = '17:18:00'; // Time of highest temperature yesterday
$WX['STAT:TEMPERATURE:MIN:TODAY'] = '39.2'; // Lowest temperature today
$WX['STAT:TEMPERATURE:MIN:TODAY:TIME'] = '06:00:00'; // Time of lowest temperature today
$WX['STAT:TEMPERATURE:MIN:YESTERDAY'] = '35.2'; // Lowest temperature yesterday
$WX['STAT:TEMPERATURE:MIN:YESTERDAY:TIME'] = '06:13:00'; // Time of lowest temperature yesterday
For the 24hr difference number display, it uses $WX['STAT:TEMPERATURE:CURRENT'] = '59.6'; // Current Temperature
$WX['STAT:TEMPERATURE:24HRSAGO'] = '59.9'; // Current Temperature value 24 hours ago.
Only the Today min and max temperatures are updated by AJAX (ajaxWCTwx.js) from the WCT_realtime.txt file, otherwise all the data is from the uploaded WCTtags.php file.