Is it necessary to change machine tensions or density of a design to compensate for a foam topper?

It is often advisable to relax tensions so you don't compress the Foam, and to reduce the top tension so that the top thread can wrap to the back. Puffy Foam works best with designs that are digitized to compensate for the thickness of the Foam, but you can use Puffy Foam for many designs that are not specifically digitized for this. Do a test stitchout first, of course, to see how well it works. This is advisable for any design with or without Puffy Foam.