@yoshiboshi It makes no sense that you normally get your period on the 6th of the month, unless you typically have a 30–31 day period, coinciding with the length of the month you are in. The pills completely regulate you to a 28 day cycle typically, meaning the date means nothing it is the day. If you begin to cycle like most do on the pill, I realize your situation is more complicated, you would get your period the same day every month. Like when I cycle every 28 days, I get my period starting every four weeks on Monday. The old style pills we would start on a Sunday our hormone pills, last pill on Saturday (21 pills) and then our periods would usually start Monday-Friday (each person was slightly different, but I could time my period to the hour). They started us on Sundays so we would have less chance of having to deal with our periods on the weekend (datenight, vacations, etc.)
I am less familar with the pill you are on, but I think the idea is similar, but with your pill it is expected that your perios will be shorter than even compared to the old style pills. I think the last few of your white pills have lower hormones if I remember correctly how those work, so that would explain why you might have started bleeding on your last white pill, the hormone level was already dropping off.
I say stay hopeful and give it a couple of more days and be sure to take your iron.