I've set up Screen Time limits for YouTube and a handful of other apps on my iOS devices, and those sync over to my Mac. On Catalina, the YouTube app limit automatically also applies to http://youtube.com.
However, that countdown appears to start as soon as I start my Mac, or perhaps when I open Safari. I did not visit YouTube on either my iOS devices nor my Mac yet, and it's already counted and hour and a half of usage, closely coinciding with the length I had my Mac started for.
Is this just buggy, or is there anything I can do to make it count only the length of time I actually visit the YouTube website?