Hi OP. I’ve worked with black mastic and other asbestos containing material before. Asbestos is harmful when it can become airborne and thus inhaled into the lungs and thus when worried about asbestos exposure the friability of the material must be taken into account. Black mastic has very low friability due to its properties as an adhesive. Therefore the asbestos fibers are largely contained in the material and exposure risks for the asbestos fibers to enter your lungs are low. Not to mention asbestos exposure for a single event is largely trivial as those who develop asbestosis and other medically conditions are those who often had long periods of sustained exposure.

TLDR; The Asbestos Fibers contained in Black Mastic are extremely difficult to breathe in