Is this a balk move?

[ump24]

Recently this play happened to me in a scrimmage. The pitcher was right handed and in the stretch. There were runners on first and second. The pitcher, with out stepping back off the rubber, spins toward first and throws the ball to second. Some may have called this a "inside move". I immediately balk the pitcher and move the runners. F1 then asks me what he did? I explain that if he is going to spin toward first to throw to second he must step off the back. He reluctantly agrees and continues on. Between innings the pitching coach comes over and asks me about my call. I explain it to him. He strongly disagrees. He says the move is legal. He says check it in the book. I cannot find in the book were it says I can call this a balk. Am I right or wrong? If so does a left hander have to step off when doing the same move with a runner on third? HELP!!!!!