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You might be applying more initial speed, but let's assume that you aren't.
The total delta_V (area under the acceleration-time curve) is the same in both cases. Placing padding under the jar squashes the curve so the maximum force isnt as high, but the impulse is longer.
Tomato paste is thixotropic, so it gets thinner under shear stress. At a certain threshold of shear stress, it essentially becomes liquid.
My guess is the quick spike ends up with less time above that threshold, so less time behaving as a liquid.