The bike had a peculiar "dance" to it. It would not even hold a straight line when in any kind of "dirty" air. (side winds, draft air, etc.)
Scab - In my particular case, I haven't noticed anything you describe. The next day after getting the tires, I probably went out for about 100 miles or so, in varying types of riding, and never noticed any pulling or dancing, including going over the Sunshine Skyway bridge which is huge. Granted the tires were brand new for me, but maybe you just got a bad tire?
Sunshine Skyway Bridge --