Well, some people just do not get their period on birth control pills. Also since this is your first month, you may just not be "normal" yet.
However, if you were having sex without a backup method, since you just started the pill, then you very well may be pregnant.
As far as that saturday/sunday thing that is just not true. Yes, that is why they have most people start on a sunday and it does work for a lot of people but not all. I usually don't even get my period until the thursday on my inactive pills and then it doesn't end until tuesday of my active pills. So for me, the sunday start ensures a weekend of a period. Kind of defeats the whole purpose of the sunday start!