99% Chance the tiles will be porcelain, riven type finish. Designed to grip feet and therefore by definition will also grip dirt. Probably one of the best jobs to do for obtaining before and after pics. The trick is to pre wet, then apply a high alkaline cleaner and allow to dwell, agitate with your rotary fitted with a medium to stiff PP brush, allow to dwell again, agitate again and then extract. Rinse and extract again. If they are really bad, add either liquid poultice or honing powder into the mix prior to agitating and agitate a little longer. Both you and the owners will be gobsmacked at the result. Finally if they will pay seal it with a good quality sealer to make ongoing cleaning easier.