What you're describing is the rear brakes locking up, causing the car to swap ends. In other words, the rear brakes are providing (proportionately) more braking force than the front.
But, think about it, if the rears didn't lock up with the Bendix/Dunlop brakes then why would they lock up with the Turner brakes (which provide more braking force than the old disc brakes)? The answer is that they couldn't.
You have something seriously wrong. I would go through the complete brake system and make sure that everything is correct.
A couple months ago I had my mechanic convert my '64 Avanti's disc brakes to the Turner system, and install his dual master cylinder kit. Everything worked out perfectly and the car has strong brakes that stop the car straight. I am quite happy with Turner's brakes & MC.
--Dwight