If I'm not mistaken the DWS is an all season tire. If you have a sport package or a Nismo you had summer tires ( not sure what comes on the base model ) so if you came from a high preformance summer tire with almost no tread and went to an all season tire with full tread you could easily feel some squirm in the steering. Also remember that tires need to be scuffed in and run through several heat cycles before you really know what you've got. I generally hate the way all season tires behave so I avoid them whenever possible, but my cars never see snow so I can get by with summer tires
The vibration should be checked out, properly balanced and installed tires shouldn't vibrate.
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