how the tension is relieved by clumping matter
The entire composite field between both fields cancels to some extent but that cancellation is least nearest the center of either field because the field varies as 1/R where R is the distance to the field center. So that the closer the two particles come together, the less overall curvature is imposed on the field. This relieves the field tension.
On the side away from the other particle's field center, both fields are mutually reinforcing because they are additive if they curve in the same direction and subtractive if the curve in opposite fashion as one would expect from the gravitational analog. The cancelling effect would cease to exist if both fields coincided exactly (but there are other forces to keep them apart).
What happens when the field pushes matter on other scales?
While the tension relief process is pushing matter together into clumps, it is also pushing the clumps of matter apart. For the apparent expansion of the universe to continue, gravity must continue because it coincides with its concomitant force pushing matter together. Therefore, both forces must scale up as matter clumps and there can be no asymptotic approach to a "crystaline universe" wherein nothing can move because it is equally pulled or pushed in every direction. Thus, stars form galaxies which form clusters of galaxies which form super-clusters and so on (though here the scaling apparently stops because the universe simply isn't old enough to have formed discernible "clusters of super-clusters".