My cat broke a bottle of olive oil on my kitchen floor. I am looking for recommendations on what to use to clean it up. We soaked up the majority of it with kitty litter. To complicate things, we had just pulled up the linoleum exposing the concrete foundation in preparation for laying ceramic tile.
Concrete is porous unless previously sealed so the oil can soak in quite deeply. You can clean the surface thoroughly and weeks later find the deeper oil soaking back up to the surface. I like your idea of getting up most of the spill with kitty litter first. That is what they do in garages and machine shops and manufacturing areas.
Olive oil can be cleaned up with water based soaps or solvent based methods. Strong liquid detergents like Wisk would do the job but create a lot of lather and the water would soak into the concrete slab. Its pretty non-toxic.
Solvents like mineral spirits will dissolve the oil but will tend to force it further down into the slab and spread out the mess before you can mop it up and can be tricky to use indoors because of the fumes.
In the olive oil industry we use bases such as baking soda to clean metal surfaces. It is non-toxic and does not impart flavors. It saponifies the acids in the oil, turning it into soap. Lye would also do this. It is a bit trickier to use but does not leave any residue or flavors on the equipment. I do not think either of these would work on concrete though.
The bigger concern is that the ceramic tile will not stick to the oily concrete. I think the best bet is using a detergent, rinsing well then using a special "glue" additive to the tile grout for good adhesion over the oily area. Your tile contractor can give you expertise in that area.