Vito told Tom to "send Luca Brasi to see me" immediately after the drugs meeting because he sensed that Sonny's gaffe would create trouble for him. Luca probably came in to see him a day or two after being summoned. No telling when Luca made his first contact with the Tattaglias, but the novel states he was stringing them along for quite a while.
Actually it is said that Luca made contact after one week with Bruno Tattaglia, at Bruno's nightclub.
"It was between the brothers Kay -- I had nothing to do with it."
