There can be various combinations, depending on when the anger occurs (or occurred) and when the singing happens (or happened). Also, the past of "sing" is "sang".
I am mad because you are singing.
I am mad because you sang the song I hated. (not "my hated song")
I am mad because you were singing.
I was mad because you sang the song I hated.
I was mad because you were singing.
I am mad because you sing it every day.
I am mad because you sang it every day.
I am mad because you sang it while I was talking on the telephone.
So, the simple answer is "no." Present effects can come from present or past causes. Of course, past effects can come only from past causes.
I hope this is helpful, and not confusing,
Bruce