I see only two waysAsami joins the Equalists. She pretends to join the Equalists a plan to spy on them, but only she and Tenzin are in on the plan. Or she is captured by the Equalists and brainwashed to join them like the Dai Lee did to Jet. Though if that first scenero happened that would cause major strief between Tenzin and the Krew especially Tenzin and Korra. They would much easier forgiveAsami than they would Tenzin would be the master mind of the plan and putting them through the emotional rollicoaster of Asami seemingly betraying them.
You have a still image of my profile pic in yours. haha