How can I locate the 2x8 boards beneath subfloor, backer board, mortar, and ceramic tile?
Assuming you do not have access from below, (if you do we have a completely different solution) you need to drill  holes in the perpendicular grout line apx 16 inches from the parallel wall to the joists to start with. You may have to drill a couple of holes until you find a joist. Then calculate every 16 inches on center and drive screws. When driving the screws, they should bite and countersink themselves if you have hit a joist.  Since you will have to re-grout the seam anyway, strip the grout and find the joists. Even doing this, I am not totally convinced a few screws will solve your problem. The best solution will be securing the subfloors from the bottom.