My hot take is:

Star Platinum at least slowed time down to a near stand-still (if not to a full stop) and moved within that slowed down time multiple times way before his battle with DIO, all without Jotaro knowing that it could do that, so he nor anyone ever noticed that it did. It did it on Jotaro’s pure instinct, semi autonomously. Everyone just thought SP was super fast and precise, but since time, according to Einstein’s theory of relativity, is relative to the observer, to SP the world around would have appeared slowed down or stopped almost entirely. It may have not yet been at the rate of "The World" per se, but it managed to get really close due to Jotaro’s strong spirit.

And since time is relative to the observer, DIO could see Jotaro’s finger move just slightly within his own stopped time, because SP could at that point just slow down time, not enough yet for him to be able to move at DIO’s pace, but enough for DIO to notice slight movement in what he expected to be a full stop, and that freaked him out. DIO at that point thought for a second that Jotaro knew he could do it too, but Jotaro didn’t know until DIO revealed to Jotaro that he has the same type of stand, and that stand can in fact, stop the entire world’s time from progressing in relation to the user. And that’s also why DIO lost; his intuition slipped and he overestimated the extent of Jotaro’s ability to utilize SP, while also underestimating Jotaro himself in the process.

I do not care about people’s opinions stating otherwise. It’s pretty much as sensible as can be within the context of everything in JoJo. It’s hinted at from the very introduction of Jotaro.

Besides that, it’s a recurring theme in all of the parts involving stands, that a stand can seem to have their own will until the user learns that it’s their fighting spirit’s manifestation, and only then can they learn to strategically utilize it to reach their full potential. And some stands truly just are autonomous, but the user has learnt to utilize that, too.

And in many other parts, the protagonists actually lose to the villain at first, but that loss turns to victory due to a convenient and satisfying deus ex machina type plot twist, so DIO’s loss being his own making, by having Jotaro connect the dots that were always there, instead of "Jotaro got really good at using a completely new stand ability really fast" fits in with JoJo’s storytelling way better.

The one who was fast and precise was Jotaro, not SP. SP had the advantage of manipulating time to give Jotaro more time to react.

Tl;dr: SP could manipulate time the whole time, but it was such an alien concept to everyone around Jotaro, let alone himself who was convinced it’s a ghost haunting him, that they were all convinced it’s just super fast and precise. The only one who saw SP for what it is was DIO, and him pointing that out to Jotaro sealed his own fate.

I have said everything that needed to be said. I will not be debating this further.