Generally speaking each Imam assumes leader ship right after the martyrdom of the previous one. Some try to justify the celebration on the ninth because it is the day after the martyrdom of Imam alAskari. Others suggest that it is the day that Omar was killed.
Historically the second Khalifah was killed in the month of zulhijjah However Omar son of Saad was killed on the ninth of Rabi’ And that could be the reason why early lovers of Ahlul Bayt celebrated