I am a little bit confused because I was playing a match where the BF4DB made a player ban announcement but the player was still able to play the game. I looked up his name here and it says that he has been banned. I don't really know much about how this works so it would be great if someone could explain it too me. Thanks.

(I have video of this too)

The server he was on is most likely set to official instead of ranked. Official servers can not kick, and thus the plugin can not kick. You could try to notify the owner of that server and ask him to set the server to ranked.

Tip of the day: use battlelog instead of the new UI. Set the server filter to "Ranked" instead of "Official". Never enter official servers again.

Official servers are infested with cheaters using gametime, a free trail they can make unlimited accounts with. Thus they can not be banned. Luckely, gametime can only access official servers and not ranked.

I just looked on the "new" UI and in the Server browser go to full filter/Type/Ranked you can search for Ranked servers only.

True, but the new UI tends to limit search results without any reason. Plus it has many bugs and has very limited functionality.

Interesting, so it will show less servers than battlelog with same filters. 

Yup. Not always, but often enough to become annoying.

No probz !