Mmhh nasty asbestos roof and i have have had my fair fill of thats stuff in my life, asbestos is a natural occuring mineral, so water will pass through the fibres once the portland cement bond breaks down over years, those leaks will release the microscopic fibres and when it drys out they become airbourne again and easily breathed in, not good if that was in uk, the area would be be sealed off and then the asbestos removed by a licensed asbestos contractors under controlled conditions using a negative presure enclosure and the ceiling reinstated. i hope you get it sorted. Peace!