No, they moved into factory, mining, retail, and other jobs that were commensurate with their abilities. The automation shift is not the same, because it will take over all the unskilled/low-skilled jobs, and there will be nowhere in the economy for the displaced people to move into.
It is not really conceivable that all these people are capable of taking on jobs which require complex thinking, judgment, creativity, or other higher skills. IQ is a real thing, and although it does not reflect on someone's human value, it does very definitely place limits on what functions a significant portion of the population can perform. And in the long run, we will all be in that displaced portion. Best that we find ways to create human security and meaning, now, for a coming world in which we have no necessary economic role to play.
There are plenty of "low-skill" jobs that nonetheless require human labor in some form because of the ability of humans -- even less intellectual humans -- to think creatively and contort themselves both mentally and physically.
Imagine a robot that does everything a school janitor can do. That simply won't exist in the near future. Sure, maybe the janitor won't have to mop large floors anymore. But there's plenty of other work to be done around a school nearly always to continue to justify their employment.
In terms of time needed to politically and socially prepare for that situation, 20 years feels really near term to me. I don't really expect our existing political structures and processes are capable of dealing with the challenge adequately in time. It's one of my top three fears for the <30 year future. And unfortunately the other two (global displacements from climate change, and bio-/nuclear-terrorism by desperate or angry people/groups) are synergistic with it. If it weren't for my normalcy bias, I'd be kind of terrified.
For how long, though? Is there any reason to think that will be anything besides a transitional stage before the robots entirely phase out the human?
I think a lot of people will be surprised at exactly which jobs too. It's not going to be the cleaners, the carpenters or the plumbers who still have to get into tight spaces that a robot butler can't handle. It's going to be the office workers that push computer bits around all day.
Any job where it all goes in and out over a wire is vulnerable. But robot manipulation in unstructured situations is still very hard, which means people are needed for their hands. I've been calling this future "Machines should think. People should work" for years. It's getting closer.