Asbestos poses a minimal threat in floor tiles. The fibers are locked into the flexible vinyl matrix and are not easily broke free to be airborne(non-friable). You can take samples of the tile for analysis to confirm asbestos. Even if asbestos is present in tile, you can use removal methods that combine wet methods (to suppress any dust), and that removes the tiles in as large pieces as possible. Do not mechanically cut, grind, saw, or sand. This will ensure that you will not release fiber.
Asbestos fiber can become a hazard when sanding and high speed buffing is performed on tiles. Most removals where the tiles are removed in large pieces have not shown large fiber counts. Using soapy water to further suppress dust, and ventilating the work-space, virtually eliminates risk. Using a cartidge filter dust mask with HEPA filters eliminates respiratory hazards. Non-friable asbestos can be disposed as solid waste in most jurisdictions.