I think he doesn't read intentions. Pudding had no intention of falling on her knees and crying, but Katakuri saw that happening anyways.
He does, only so far into the future (relatively speaking in One Piece context anw. Compared to superpowers that can predict things hours or months in advance in other fiction, calling this ''so far'' is kinda ridiculously insulting LOL). That's why I'm trying to explain it by using the word ''natural''. If things proceed naturally, then even if the intention has not formed in one's mind yet, the action still inevitably comes. Because sooner or later that intention would come into existence anw, and then the action.
So yeah, unlike several other CoO users we have seen, Katakuri doesn't just start reading intention the moment it appears in one's head, but he still reads intentions, only that he reads it in advance, like a logical follow-up of the intention/action before that and so on and so on, up to what he is currently seeing (it goes backward, if you know what I mean).
Because, how can he not read intention? It is CoO, so of course the mechanism is that of CoO, otherwise it would just be a different ability. Bege's words demonstrates that clearly and literally: ''he honed it so much he can see a bit into the future''. So it is reading intention, only that far ahead.
Btw, we have been using reading intention but I think the correct term is still listening to body's voice that Ganfor said in Skypiea.
He literally sees the future, but from the moment he interferes, the future changes, which is why Luffy is able to dodge him, but not hit him
No, Luffy dodged him because...he simply could react and dodged him. Remember that Katakuri already changed direction and attacked the position Luffy dodged to (which means he can still see the future at this time, which makes sense because that's what even normal/base CoO does, predicting immediate movement), which is why Luffy said he was twice as beat: he has to dodge twice. It's just that even when Katakuri changed the attack, Luffy can still react fast enough to dodge again whereas Katakuri can't repeat a second time. This is different from the limit we're talking about.
Clearly close combat gets same treatment like it does back in Skypiea or past arcs. If every time he makes an action, Katakuri is unable to see the future for a bit of time, then his CoO is only for defense and that's canonically false, cause like I said above, he used it to attack where Luffy would dodge to.
I think it's only considered ''changing the future'' in certain cases and we have seen them. But what the common trait between these cases is and how exactly this works I don't know. The only idea I have is maybe in those cases, the change is big enough to shift the future onto a different enough path (this starts to sound like Steins;Gate LOL and I am not sure if Oda puts that much thought into it. He's not the physics type. Hell, maybe he just does it as he likes for plot/choreography convenience, which means all these explanation is for naught )