The thing is, Dio is actually very calm and level-headed around most people, and good at rational thinking. When Joestars get involved, however, he tends to flip the fuck out.

Dio was just trying to look cool and smart, so Pucci can be like "Omg this Dio dude is such a good and smart guy, I would reset the universe just for him"
Meanwhile he was thinking "but my stand is the strongest stand! Wryyyyyyy!!"