2005 Subaru Outback vibration when starting from a standsti

Suspension problem
2005 Subaru Outback 4 cyl All Wheel Drive Automatic

Hello. When starting off from a standstill and immediately turning either direction, I feel a vibration. Happens in reverse as well. Had mechanic check it out and after pretty thorough inspection of suspension and wheel bearings, he felt it was the barely legal worn tires that may be the cause, though show no unequal worn areas. Put snow tires on this week and vibration still there.
What could be the cause? Thank you, rosie