Zemo is on of the best villains in the genre.
Zemo doesn't have a master plan, he calls audibles the whole way through and is looking for evidence he knows will tear the avengers apart.
Zemo's first plan (interrogating the Hydra agent) didn't work. The Hydra agent told him nothing and took the "1991" information to the grave. So Zemo's next plan is to get the international intelligence community to find Bucky, because Zemo does not have the resources to find him himself, How does he do this? By framing Bucky in a terrorist incident, aimed at the Accords, knowing their full resources will be used to find Bucky. Why does he need Bucky? To tell him about the details of the "1991" mission, to have Bucky tell him where the tape is showing the assassination of the Stark's, where the facility is that created him. That's why he needs the book with the activation words for Bucky that he got from the Hydra agents home, because Bucky is not going to tell him, if he even remembers, but a controlled Winter Soldier will.
That interrogation scene with Bucky is the only plan of Zemo that works out the way he wanted.
Steve, Stark, and Bucky showing up at the end was not part of his plan, but since he has them there and the tape of Stark's parents death, it's as good a place as any to use it.
-Every piece of dialog supports this, Zemo knows he can't physically hurt the Avengers himself "Stronger men have tried and failed".