He did meet Massino, just they were never close. Massino used to brag he was always wary of Donnie, but I don't think he ever had a sixth sense about this or anything, it was just the rivalry between crews... he had his own crew and Sonny Black and him soon drifted apart and became rivals for the top spot of street/acting boss.
Massino was already a powerful capo by the end of the Donnie Brasco operation.

Pistone describes in his book Unfinished Business the meeting with Massino. They just shook hands and introduced, that's it. He was relieved because in an earlier case apparently he'd been one of the agents who had arrested Massino.