When does my birth control become effective?

Hi all, I have been taking MonoNessa for close to three years now and I love it for regulating my period as well as extra insurance against pregnancy. I was just wondering: I know the drug pamphlet and all of the health sites say that when you are a Sunday starter, you should use backup protection for 7 days when first starting the pill. What about after being on it for a while? I am a Sunday starter and my period comes on Tuesday or Wednesday, so Sunday is always within 5 days of starting my period. Does this mean that my birth control is effective right away, or not? If not, would you recommend me switching to a day 1 start next cycle so that it is effective right away?