After reviewing the demo the real problem is what occurred to you and is mainly an issue of the length of ban. You should not have been banned for more than 10min for that. From what I could see from the demo you were in the server for long enough to grasp the situation which during you made a comment that undermined an admin and disrespected them at the same time. An admin can ban you in conditions like this when there are a few players at the same time causing problems. If it had been just you by yourself you would have gotten a warning and or been muted.
It is like when the police are arresting someone, in many cases anyone who gets too close to the arrested is also arrested. This is because during this time the primary function is to reestablish order. You have 1-2 players that are not listing to an admin and then a 3rd one jumps in and says something like that they are going to get banned.
Now the one issue I do see could be that the admin did not know how long you had been in the server. This is likely why you did not get any warnings b/c they assumed that you were in there when general warnings were being issued.