You can tile over terrazzo, but there is a process you must follow. Most terrazzo floors are cement, but others contain epoxy and different resins. The floors are coated with acrylic or wax finishes after they’ve been polished. Many surface coatings are bond breakers, so you’ll need to remove them first. You might have to mechanically abrade the flooring to obtain a high level of adhesion
You’ll also need to figure out the grout and mortar application with your contractor. If your terrazzo flooring has pre-existing cracks or signs of potential separation between the flooring and metal divider strips, an anti-fracture membrane may be required.