Frankly, the term "spring cover" is a marketing term to divert your attention away from the true purpose of this piece of fabric.  It is a misnomer to disguise the real reason for it's existence.

The true purpose of the "spring cover" is to deflect your foot away from the bullhorn of the mat cleat.  For many years, all rebounders used a bullhorn style cleat which had a metal end that protruded between the spring sets.  The metal "horn" was used to keep the cleat from sliding out from the fabric tabs.  You still see this sort of cleat on cheap Asian imports.  The bullhorn allows the mat to be produce cheaply as it does not need to be precisely positioned.  Mat production speed can be increased significantly due to this sloppy mat construction.