Does your sewing machine have a "lip" on the edge of it?
My sewing machine cabinet has a hinged section, so that you tilt the machine up, and fold the hinged section down, then the sewing machine sits on the table, not on a lower piece attached to the table. I've never had a vibration problem with the sewing machine cabinet/table.
But I have had major vibration problems with a so called craft table made out of plastic. The table and machine jumped all over the place.
I think your problem is lack of support on the surface where your sewing machine is sitting.