Ah, my favorite wringer washer from when I was much younger. I would spend every Monday that I could downstairs watching my mother use that machine.
I don't know if other people used them the same way as she did, but she would fill both tubs with water and detergent, one tub with hot water, the second tub with warm water. Then she put each load of clothes through both tub for aboput 10 to 15 minutes per wash tub. The clothes would be first washed in the hot tub, and then she would put the clothes through the wringer, letting the clothes fall into the second tub while it was agitating. It was so fun to watch the clothes slowly but surely be pulled down into the second washer as it agitated.
For rinsing she only used the laundry tubs that we had.
Hope this helps.