No, you do not have to worry about new popcorn ceilings having asbestos. All residential building materials used since the mid-1980s stopped including asbestos, so new popcorn ceilings have no risk of asbestos. You can still create a textured drywall ceiling with a popcorn texture if you like, but new techniques have no risk of adding asbestos. 

Asbestos fibers can stay airborne for 48 to 72 hours, depending on the home's ventilation. Fibers can linger longer in enclosed spaces with poor airflow. Because the fibers are microscopic, they can easily remain suspended, making them difficult to detect without professional equipment.

Epoxying over asbestos tiles is generally considered a safe option when done correctly. Epoxy acts as a sealant, encapsulating the asbestos tiles and preventing the release of asbestos fibers into the air. The key is ensuring that the asbestos tiles are in good condition, firmly adhered to the substrate, and not damaged or deteriorating. This method is only appropriate for tiles that are undamaged and securely in place. If the asbestos tiles are already loose, damaged, or deteriorating, encapsulating them with epoxy may not be a sufficient solution, as it might not address the potential for ongoing asbestos exposure.

If you can locate building records, you may be able simply to see what type of tiles (or bonding agent) was used. Any flooring made between 1950 and 1989 more than likely contains asbestos. Asbestos tiles can also be slightly thicker than other tiles and often measure 9” x 9”, 12” x 12”, and 18” x 18. Black mastic was a commonly used adhesive that contains asbestos.