Turntable Causes Speaker Cones To Excessively Move Rapidly

Hey, big news flash. I thought maybe it could be the rubber mat. I tried plaing a record without the rubber mat and I did not notice any woofer movement!

It is the stock rubber mat that came with the turntable. What are ya'lls thoughts about this, please?

@dman777 did you re-adjust VTA after you removed the rubber mat? 
The only explanation for this is your VTA  was completely off with the mat and now the arm is in a more proper position. 
When you look at the arm with stylus on the record, is the arm parallel to the record? With and without the mat. 

@audphile1 no, I did not readjust the VTA... I had it at 0.5. but one thing is interesting is that on the rubber mat when I watch the platter turn, the lip does have a slight wave in it... There’s a area where it goes up about 1/8 of an inch... Like a hill. Maybe for about 2 inches in length. It’s not much but I’m wondering if this is why?

Yes that would prevent the record from being coupled to the platter and would cause the vibrations.