In his defense, Jay did have every reason to believe both he and Angela were going to die when he dropped the truth about Marcus’ death on her, but he also underestimated her reaction because he was not expecting her to shoot him right after he’d saved their lives.
Although Jay was working to save her life as well as his own throughout the winter finale, her survival is a pretty big inconvenience for Intelligence, the CPD, and Jay himself if he survives thanks to his decision to come clean to Angela.