We have always just used Dawn dish soap mixed into the water pail. Rinse good, let dry, oil well, and set in sun to dry, and soak up the oil. Now of course that's with leather. Synthetic, do the same, except skip the oiling.
The fact that synthetics do not require the same care is one of the popular selling points of them - all you need to do is wipe it down with water (soap if necessary) and dry it off. Using any of the traditional saddle care products used on leather goods will damage your synthetic.