If Monday is the second day in the week, why "juma|tatu"? What am I missing?
The Swahili week relates to Islam the way that the English week relates to Christianity. Sunday is the traditional beginning/end of the week. In Islam, Friday is the day to listen to sermons. Jumamosi (mosi is archaic for first) is the first day after, Jumapili is the second (pili) day after, Jumatatu is the third day after, etc. Alhamisi (Thursday) is from Arabic, and so is Ijumaa (Friday). The week begins again on Saturday.
But nowadays the work week starts with monday even in Kenya. Probably due to internationalisation.
The day that starts the week is highly cultural and will differ even among countries that speak the same language. See USA vs. UK.