Birth control

So I’ve just started on the pill for the first time ever and my doctor said to wait to count on it as birth control until after the first month. Well yesterday was my last dose of the first month’s pack and my fiancé and I had sex and he pulled out like we always do because we weren’t sure if it had been long enough on the pill but he’s kind of worried that he didn’t get out all the way in time. Since I was already on the placebos and finished with the active pills are we okay or should I get plan b? We get married in 6 months and my family is very against having kids outside of marriage. Can someone put my mind at ease? Lol