Varying hormones over the menstrual cycle, from normal, baseline, to ovulating, back to baseline, then premenstrual, then coming on, can cause changes in insulin requirements through the month. It could just be that your insulin dosage matches your insulin requirements for when you are on and that's why you find control better during your period. I certainly used to need different basal rates for ovulation and premenstrual sections of my cycle. I've only, fairly recently, started having periods again after a long time off so hormones seem to be having a more gentle effect so far.
Being on the pill also changed my insulin requirements, with an increase of about 50%. Although it was a little more stable once the increase was in place.
Insulin is a hormone. The action of insulin is impacted by what other hormones are whizzing about in your body. So if the hormones in your body change, either because you've stated/stopped taking the pill or because you notice an impact at different stages of your menstrual cycle, it makes sense to do a little assessment to check basal rates and insulin to carb ratios suit your needs for when those hormones are in play. Although that can mean having 5 different basal rates set throughout the month, which if you are particularly hormonal from your period might make you vaguely homocidal!