By rinsing, you can only remove stuff from the surface and slightly below. You need to remove molecules which sit in the pores of the stone.
Chemically, you are working against diffusion and adhesion. By washing with soap, you have deposited a number of molecules onto the stone surface, these have diffused into the numerous pores of the solid. Now, these molecules cling there by means of adhesion, which makes it really hard to get rid of them.
Thus, instead of just rinsing, let it sit in a bowl covered with warm to hot water.
Heat and time will allow the molecules to slowly "come out of the cover" and go into solution instead. This is driven by the concentration of soap in the solution (you want little to none) and temperature (you want it hot!). Preheat the stone if you can.
Add a drop of oil to the liquid, and disperse by beating with a fork (or anything comparable - the idea is to have as many small droplets as possible). This will act as a trap for the soap molecules in the water and reduce the solute concentration - increasing the pressure for the remaining adhering molecules in the pores to go into solution. If possible, try beating foam, and if some foam forms, then remove that and introduce new oil.
I suggest somewhere around at least 30-40 degrees Celsius and a timeframe of 10-30 mins.
These are just guesses. Also, depending on what material the stone is made of, there might be additional reactions and/or interactions involved that could require a higher temperature or longer times.