See, if you only have read the Foundation Trilogy (or maybe even only the first part), Seldon seems to be this all-knowing oracle, appearing at seemingly random intervals, and acting like he has everything planned out. I can't tell, what about the stuff that was later elaborated on was somewhat in Asimovs head from the start (honestly, probably not much, I think he just rolled with that basic idea he had), but it is made clear that Seldon is simply the person who thought about the idea of Psychohistory, and had then a team of mathematicians, historians and psychologists to work on it.
I will probably mangle, or at least explain badly, some statistical concepts. Sorry if I do, the basic ideas should be correct. I hope.
It's not like Psychohistory is something that you can use to perfectly plan out a course through the future. It is basically not that different from something like a linear regression, where you try to find a correlation between x and y (while, hopefully, remembering that correlation is not causation). It's a model, that uses existing data to extrapolate. If you find a correlation, you might be able to say "if x develops that way, y might, with a good chance, develop that way". The idea with psychohistory is just that, maybe, you can do the same thing with groups of humans. The basic idea is the same.
Psychohistory takes a ton of data, about which factors created which situation. With all this information, Seldons team could then play through different scenarios, to find out what they could influence to reduce the amount of time, until a new, strong Empire (or some other intergalactic body) could arise. In this case, it was simply to make sure that you have a group of people on Terminus, far away from the center of the Empire. This group would then be in a situation, where certain things would happen. But never perfectly sure, just with a certain probability.
Seldon never is a master manipulator. Granted, he manipulates people around him, but that is on an individual level. He never thinks, that he can perfectly predict the future. He just tried to create a mathematical tool, that would give him insight and therefore show him a way to, maybe, help civilization not collaps for 10000 years, or something. The predictive power of his model might be too strong, but that is just a basis for stories, that Asimov found interesting. But Seldon doesn't guide anything, he just made a very specific change (creating the settlement on Terminus), as this gave the highest chances. He calculated everything from there, with the clear knowledge that there was a margin of error.
As mentioned, Asimov grew bored with this idea, and basically shot the idea that Psychohistory would ever work to pieces himself. First, by using the Mule, a mutant, as a variable with a lot of influence, but also something Seldon couldn't use in his model, as he had no data for it. Which was always part of Psychohistory - the small, but existing, chance that the model wouldn't work. Seldon himself knew, that there was no 100% chance for that.
Later, he introduced the Second Foundation, a small group that could manipulate minds and were always there to make sure that, if something wasn't going according to plan (so if we were in the 1% chance of failure of the model), the problem would be corrected. It is made clear, that the influences were very small, and that this was just the correcting force, to make sure the Foundation would stay inside the probability of success.
Further on, we learn of another force, that also did some manipulation of this type. And that is ignoring the fact that, as time goes by, the predictions get less accurate. Which makes sense, as the possibilities keep growing.
Point is, even in-universe, it is made very clear that Psychohistory is flawed and needs additional help.
Ok, I'm rambling here, and not quite sure if I even got to your point anymore. I guess what I dislike is, that Psychohistory simply isn't what the show thinks it is. It's not this way of predicting the future perfectly, but to make predictions with a certain margin of error. The model in the books might be too strong, granted, but the idea simply came first. Psychohistory was just a tool, for the author.