1 base or 2 bases?

[BktBallRef]

From another board:

"Last year, one of our pitchers attempted to pick off a runner at first base, but the ball got past the first baseman and went out of play. The umpires awarded the runner third base. We argued that the pitcher had used a jump turn (i.e. simply spun and threw) and that since he had not stepped off the rubber, the runner should get only one base. The plate umpire said that the pitcher had disengaged from the rubber by making a jump turn and that therefore two bases were warranted.

I think he was wrong. In fact, his father (who is also an umpire) had explained the bases-awarded distinction to me by contrasting the stepoff and the jump turn. He said the tradeoff with the jump turn is that the runner is awarded only one base if the ball goes out of play, but the pitcher also runs the risk of balking if he doesn't spin toward first base. Does the rule book define "disengagement" from the pitching rubber, and if so, what does it say? Last year, one of our pitchers attempted to pick off a runner at first base, but the ball got past the first baseman and went out of play. The umpires awarded the runner third base. We argued that the pitcher had used a jump turn (i.e. simply spun and threw) and that since he had not stepped off the rubber, the runner should get only one base. The plate umpire said that the pitcher had disengaged from the rubber by making a jump turn and that therefore two bases were warranted.

I think he was wrong. In fact, his father (who is also an umpire) had explained the bases-awarded distinction to me by contrasting the stepoff and the jump turn. He said the tradeoff with the jump turn is that the runner is awarded only one base if the ball goes out of play, but the pitcher also runs the risk of balking if he doesn't spin toward first base. Does the rule book define "disengagement" from the pitching rubber, and if so, what does it say?"

Thanks in advance.