Even when you put hair dye on your hair, few drops of dye usually spill on to the floor or walls.
So, you cannot really control this occurrence; the only solution is probably to dye your hair in a beauty salon. However, there are several ways to take the stain off from the tiles. The only thing you should remember about removing stain is that you need to act as early as possible.
Thus the best idea to remove these drops of hair dye will be to wash them off immediately with plain and clean water. So you should keep a mug or glass, filled with water, in front of you when you work on your hair. Secondly, you must keep an eye, whether any drops or droplets have spilled out from your hair.
However, you might miss some of them, which will make the stain darker and stronger on the surface. There are abrasive cleaners containing a percentage of acid, which will immediately take off any kind of stain, but it will surely damage the glossy finish of your tiles and make them look more dull and worn. It is always suggested to test the new brand of cleaner on a small or unnoticed part of the tiles to see its effect on it.
Otherwise, there are some other remedies for this problem. You can safely use bleach to take care of this stain. Sprinkle bleaching powder on the stained area and keep it soaked overnight before you wash it off. In case of your bath tub, you may fill the tub with water and then add the bleaching agent to it.
If the stain does not get off in one try, then you have to repeat the process for several consecutive nights. Alcohol is also known to be very effective to clean up the stains on marble tiles. Alternatively, you can talk to your beauty salon or search from net, to purchase the dye or color remover, which will definitely work for your tiles.