After the events in WS, Steve was trying to find Bucky, to bring him in, to help him. That was his priority. Zola had merely hinted that HYDRA had something to do with Howard's death. So the first time we, the audience, sees that Bucky verifies that he did all those things that HYDRA brainwashed him innto doing is on the quinjet to Siberia.

Please tell me, given that timeline, when Steve had a chance to tell Tony what he knew?

No, I get it. You're not going to forgive Steve. Got it. But understand that some of us have thought about this and know that Marvel made this an immovable object/unstoppable force paradox. They both lose. No one wins.