I cannot really say why this is happening without testing it myself. Nobody else has reported this as an issue.
It may be that the site itself has some kind of auto-detection ability and messes with the recording.
Have you tried using all of the different recording modes in Screen Recorder? The most straight forward and problem-free one is Region, so if it does not work with that then it suggests that something is interfering.
If you would like me to look into it further, please supply a link to a video/site that causes this problem for testing.