I would also like to know how old you are as I think age makes a difference when it comes to BCP. I took Yasmin (which I think is the same as Yaz but a bigger dose?) when I was 17 and I don't recall remember getting an initial break out. I was on it for about 4-5 months and it did help my skin though not 100% cleared, although I've never had cystic acne. The only reason I went off it was because I didn't have a need for contraception anymore and I had never meant to take it for my skin anyway. My skin stayed pretty much the same after that, no crazy breakouts or anything. I got some pretty weird side effects like intense cramps and rashes. :/
I'm on Diane now which has almost cleared my skin to 100% but I don't know what the consequences of going off that will be like since I'm 24 now.