I don’t know much about poison oak - poison ivy is much more prevalent here in Michigan. I’m told that the urushiol oil soaks into the skin in about 10 minutes - if you can’t wash it off before then, you’re likely to get the rash. After that, scrubbing will not spread it - that’s an old wive’s tale. My guess is that people thought it was spread because the rash developed and blossomed over time after they scrubbed, and so it looked like that was the case.
A blow dryer on the area works like the hot water. I could blow dry my arms before bed at 11pm and not wake up itching until 3 or 4 am.
The other thing that helped…Preparation H.
BZZZT! wrong. I was riding my mountain bike and my right leg brushed some plant at speed. A couple of days later it started to itch. Bad.
Washing it off it in the shower didn’t help. the rash spread. and spread some more.
Several days later I put 2+2 together and used fels naptha soap to do away with the oil.