How to prevent chain looking dirty one ride after cleaning it!
Wiping off excess oil with a rag is good, but there will still be extra oil hidden inside the links in-between the roller and bushings.  This is what comes to the surface once you start riding. You can try spinning the drive train a bit (to bring this oil up) before wiping down a second time. Typically, you will need to wipe the chain off again even after a short ride.  Personally, I prefer a thicker oil, so that after second or third wipe to get the chain really clean I don't touch it again for a couple hundred km. A lighter oil needs to be applied sooner, meaning less time running clean.

Also, when you spray with water it typically takes longer than an hour to dry the water inside the links.  As such, when you are adding oil it may not penetrate as well due to water being in the system.  This could further contribute to the dirty mess you are seeing. Using solvents on the chain too early also removes the factory lube (typically a type of wax), which reduces chain longevity. In terms or real world use I measured a 30% reduction in chain life if you strip the factory lube out early. As the chain gets older, less factory lube remains and cleaning with a solvent becomes a non-issue.