Is it okay to wash a plate at a later point?
That quote sounds like they're assuming you fill the sink with water and leave dirty dishes sitting in the water. That seems gross. And of course you should wash your hands after doing the dishes, regardless of whether you washed your dishes immediately or let them soak first.
I frequently leave dishes to soak and wash them later, but I don't fill the sink. Just fill the dish with water and let it sit in the sink. When you come back to wash it, dump out the soaking water, and wash as normal with soap and hot water.
Some dishes work best if you rinse them right away, then let them soak after rinsing. Oats tend to dry on rock-hard, so be sure to wipe off any smears that are above the water level before leaving it to soak.