Actually no. He was made an ANBU captain at age 13 as said by Kakashi. And obviously that means he was still in the village at the time. The massacre came not that long after that.
he didn't fight oro after leaving the village, he fought him when he met tobi , at around 11... He BECAME a captain at 13, he joined anbu at 10... and the police men said half a year after joining anbu his personality changed.....so he got the mission at 10.5
He found tobi whenever around that time and they didn't start the mission till he was 13... 3rd hokage was still trying other methods, etc
Go find the two manga pages where sasori and kisame both say itachi was 11... Hint, 1 of them was at the end of part 1