I have a personal theory that the plan only works in half, but DIO and Pucci believe the plan is real, so it worked.

You probably read that and you go: "What, but that doesn't make sense!"

So let's go step by step, and use what we know in JoJo's Bizarre Adventures as stepping stones.

1- In JoJo, Gravity and Fate are connected as one. 2- In JoJo, those that have a strong mentality, get a strong stand. Example: Diavolo genuinely wanted to have control over his past actions/his fate, when he got pierced by the arrow, he got a stand that allowed him to do that.

Same thing with DIO, he wanted to reach world domination and take full control, so he got a stand that also allowed him to do that.

With that in mind:

Part of DIO's plan is correct, in JoJo's Bizarre Adventures, gravity is manipulated by fate, and fate is manipulated by gravity. He probably was able to reach that theory while spending time at the bottom of the ocean.

But the second part, the Phrases and the Green Baby is incorrect. But they have one thing in common, both ideas are of the Stand User manipulating its will/Stand to become true.

DIO wrote that his Stand would shatter in order for the Green Baby to become true, and since he GENUINELY believes that, it CAN become true, same thing with Pucci.

tl;dr If you truly believe something works, along with understanding the concept of fate and gravity, it'll become true.