[Moved to Audio & Security.]
First off, welcome to HAN. :cheers: I moderate the Integra forum, but I've moved your thread here as a matter of policy.
I run a set of Infinity 625i speakers in the rear. While they're a bit shallower than your Panasonics...I've never had any problems with vibration.
My bet is that the speaker itself is vibrating against the plastic mounting "basket" because it's a little too deep to fit flush..
I'd check to see that the speaker mounting flange is seated fully and that the screws holding the mounting baskets are tight. You may need to trim the plastic mount to clear the speaker magnet. Assuming the speaker fits properly, torque down the mounting screws at all points.
That ought to take care of it.
Welcome to the board.