Dio has tangled himself with the Joestar kin and destiny. Due to this, he knows they know of him and he knows he must kill them. What I find fascinating is how he does this. Stands are linked to breath, just as hamon, and it makes me think that Dio couldn’t vampirize stand users without debilitating their strength; the stand. That said, he does have the ability to brainwash people which would keep their abilities in tact, or he could simply persuade them as working under a powerful man doesn't sound so bad. Further, Dio having a stand(perhaps linked to Jonathan) and being able to use it, assuming it’s akin to hamon, leads to even more questions.
Kakyoin is interesting, when we saw his power from afar, it made it seem that he could have simply sliced Jotaro’s throat without going near him. Yet, he approached Jotaro, making his presence known. Then, obviously, this was enhanced, the handkerchief that he gave Jotaro literally announced that he would be killing him with his stand. Perhaps a sense of honour or pride is in our midst, someone who may use an inherently dirty stand but nonetheless isn’t a sneaky assassin. He showed us that he knows Jotaro well, he was aware of Avdol and his stand and he tested Jotaro's stand before going into battle, observing the data. And his stand is Hierophant Green, it acts as a parasite, attaching itself to an individual and being controlled from afar, literally having nestled into the nurse’s mouth. He seems to be able to use physical means, be it paint or a puppet to control it which is surprising as, with it being a manifestation of life energy I’d assume it acted on his feelings and desires.
Regardless, after a horrific pen-eyeball stabbing, we saw the stand makes who it possesses stronger in a frightening way, similar to ACDC with Suzie Q. Jotaro showed the good hearted, woman protecting side of the Joestar blood and refused to let her be harmed any further, kissing her to pull out the stand in beautiful Devilman fashion! Overall, this also denotes, with assumedly Dio sending minions to kill Jotaro he’s put on the role of the reactor. If he doesn’t kill Dio, Dio will kill him, or at least pester him for the rest of his life.