Hi there G_Qin,
Thanks for the reply and those additional details! So you have downtime set to block all apps when the time limit is reached, but Twitch seems to continue operating once the limit is reached on your Mac, correct? You mentioned downtime is set to block all apps; have you found this happens with other apps, or only Twitch?
It might help to try setting up a temporary administrator account and then sign in there to see if you can replicate the same behavior with Twitch and Screen Time. Here's how to Set up users, guests, and groups on Mac.
Let us know how downtime works with other apps, and what happens in the test administrator account. That will help get to the bottom of what might be happening.
Have a good day.