Zemo could of known that Stark knew about his location OR even his intentions..... I would of half-expected he would knew Rogers and Bucky... I would of even accepted that. But he was expected Stark to be there to show the tape... HOW?
And as for Captain America... the ONLY thing that made sense is his relationship with Bucky. That was his ride or die. That's never even questioned. But everything else is. For copping pleas over how the Avengers consistently cause collateral damage, something he always chastised Fury in initiating, to holding that secret to Stark.... his moral character never been compromising yet he made a compromising decision that is against his character. That sappy voicemail apology not standing. It would of been totally IN character had it been Stark holding onto a secret to Rogers that would of been devastating. But either way... that last reason of the final battle was FORCED...just so there be a reason for them to fight one more time. Made little reasonable sense when Stark already knew that Bucky wasn't under his own control.
Imagine if it was the Purple Man from Jessica Jones, able to control other minds... would you emotionally say, "fukk that, he still killed my mother" regardless of you already KNOWING the truth of who's behind it?
Your missing a few dots to connect. It didn't matter if Stark was there or not, his actions would still be the same. Why did he leak that the real doc was dead, complete with disguises as Bucky? Once he released it, the Avengers would be united to try to stop HIM because they think he's trying to awaken the other sleepers. Whoever is there, once the tape is shown, they would bring Bucky in or completely step out of it. Cap would not let them take Bucky in, so now the team breaks up indefinitely. MISSION ACCOMPLISHED.
It's not about collateral damage, because he understands that it will always be that. They try to minimize. In every Avengers, AOU they always tried to evacuate before engaging. He feels that it's best that the Avengers operate outside of govermental control, for reasons being of being hired guns. His beef with Fury was not the secrets but what the secrets actually were - black market WMDs. Fury was stealing and manipulating alien technology to create weapons that could end up in the wrong hands..basically Stark pre-Iron Man. Every mission he sent them on, he had a hidden agenda to not destroy, but steal. He would tell them one thing, but do another. That's what makes Cap different. By this point Cap knows that Howard was killed by HYDRA, so does SHIELD, Widow, even Tony already knew that. Winter Soldier was one of the agents that completed such missions, so they all put 2 & 2 together. But no one actually knew that Winter Soldier actually did it, or the extent measures he took to kill them, or knew that video existed. Once you see the video, it's an entirely different ballgame, so they would all have reacted in some way. "I didn't know it was him" was Cap being honest. Cap isn't against secrets, it's hidden agenda secrets, which is why he apologized with the letter. But he's moreso about protecting people, protecting everyone at the same time.