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Joe is exactly correct; the trim tab should be adjusted so there is equal steering effort in both directions. That is what it is for.

In your case, you need to move the trailing edge of the trim tab to starboard to make the steering more balanced.

But to answer your question, no, the trim tab will not be affecting the vibration.

I think that since you have the motor on a jackplate, the next thing to try is lowering the motor 1/2 inch.