The tubes are nothing to do with periods. They are responsible for the site of fertilization of eggs. The periods are coming from uterus. The inner layer of uterus is called endometrium which has a1 mm thick layer called basal layer. This basal layer respond to the circulatory estrogen and progesterone. When there is no fertilization all this preparation of endometrium is wasted in the form of periods.
Because your ovaries are still producing eggs and it is the release of an egg from the ovary which triggers hormones to start your womb preparing for a fertilised egg. When no fertilised egg turns up, the womb lining falls away (this is what you see as your period). Just having your tubes tied will not stop your egg production and therefore will not stop your periods. Periods are a nuisance, to say the least, but it is better to still have your ovaries working normally, as the hormones from this keep you young.