The main advantage of self-adhesive tile is right there in the product name. The tiles come with adhesive already applied to their backs. Backing paper covers the adhesive on the backs of the tiles. To install, you merely peel the backing paper away from the tile back and press the tile into place, much like a sticker. The adhesive layer on self-adhesive tile is thin, though, which doesn’t provide space between the concrete floor surface and the tile like mortar does.
The main problem with installing any type of flooring directly to a concrete basement floor is the moisture absorbed from the soil. Since concrete is a porous material, moisture passes through the concrete to any flooring laid on the surface. When installing flooring on a concrete floor, especially in a basement environment, you should use a sleeper system along with a moisture barrier.
As the moisture from the surrounding soil passes through the concrete surface, it gets into the adhesive backing on self-adhesive tiles. This causes air bubbles in the adhesive, eventually breaking down the adhesive. The popping sound you hear more than likely stems from this destruction of the adhesive. As the adhesive stops working, sections of the tile may pop off the concrete surface.
The only way to permanently repair self-adhesive tiles that make popping sound on a concrete basement floor is to remove the tiles, build an appropriate sleeper system for the flooring, then relay the tiles. A sleeper system consists of a plastic moisture barrier against the concrete floor and a series of boards -- at least 3 inches high -- that cross the floor’s surface. The boards are covered by pieces of plywood to create a secondary subfloor 3 inches or more above the concrete. To reinstall the self-adhesive tile, you'll need additional adhesive.