Why are the tribunes Falvius and Marullus punished?
This is a great question. A little context will be necessary. In the beginning of the play, both Flavius and Marullus give the commoners a hard time for wanting to cheer for Julius Caesar. These two men (tribunes) do not like the crowds fickleness. Were they not cheering for Caesar's opponents in the past? Moreover, they do not like the fact that Caesar defeated another Roman in civil war, rather than a foreign army - not to mention they feel threatened by Caesar's power.
As the play progresses, the crowds begin to love Caesar more. There is a statue of Caesar and it is decorated to honor him. During the triumphal parade, Flavius and Marullus take down the decorations from Caesar's statue. When this is reported to Caesar, they are both punished. In particular, they are removed from office for this action.