Your kids should not be able to access the YouTube messages app when the full YouTube app is not on the phone. However, it appears that as long as the full YouTube app is on the phone, even if it is restricted by Downtime, the YouTube messages app can still play videos.
I would suggest submitting feedback to Apple here: https://www.apple.com/feedback/
In the meantime, if you do not want your kids to be able to access YouTube at all try the following:
Delete the YouTube App and YouTube Messages App. Then go to Settings > Screen Time > Content and Privacy Restrictions > iTunes and App Store Purchases > make it “Always require a password.” (As long as your kids don’t know the password.)
Other options include restricting the ability to download apps or lowering the age of allowed apps (YouTube is rated 17+).
Note: I was able to restrict access to YouTube with the above steps, but I do not use Family Sharing and do not know if that changes anything.
-AJ