Screen time not blocking TikTok

My son doesn’t even have TikTok installed on his phone but if someone sends him a TikTok through iMessage, he can watch unlimited TikToks. Would love to know why this is all happening?

Go to Settings and tap Screen Time. Scroll down and choose your child's name under Family. Tap Turn on Screen Time, then tap Continue. Set up Downtime, App Limits, and Content & Privacy with the limitations that you want for your child, or tap Not Now.

Use Screen Time on your iPhone, iPad, or iPod touch

Go to Settings > [your name] > Family Sharing > Screen Time. Tap the child you want to set up Screen Time for. Tap Screen Time, then follow the onscreen instructions. For information about Screen Time settings, see Set up Screen Time for a family member on iPhone.

Set up parental controls with Family Sharing on iPhone

Follow these steps:

1. Go to Settings and tap Screen Time.
2. Tap Content & Privacy Restrictions and enter your Screen Time passcode.
3. Tap Content Restrictions, then tap Web Content.
4. Choose Unrestricted Access, Limit Adult Websites, or Allowed Websites.

Use parental controls on your child's iPhone, iPad, and iPod ...

I am not sure how have you set time for Down Time.

It would be better if you can please post a screenshot, in order to understand the phenomenon better. Images / pictures speak louder than words. See the pic below