You certainly shouldn't be hearing any type of noise when walking on your tiled floor, other than the solid "thunk" of your feet hitting the tiles. If you hear crunching, popping, or creaking, this would indicate that the bond beneath the tiles has failed. This can happen for a few reasons, all of which will be detailed thoroughly in this article.
One common reason for this to happen is improper preparation of the substrate. The tile contractor needs to make sure first and foremost that your subfloor (plywood or OSB) is securely fastened to the joists below. If your home is like most, the builder probably didn't bother using adhesive and screws when securing each sub-floor panel. They nail them down quickly with a nail gun to save time and money. A good tile installer knows this, and will always screw down your sub floor using appropriate flooring screws to ensure strength and rigidity. This step alone is extremely important and is overlooked by many installers looking to make a quick buck. A good tile installer will also use the right screws; construction grade screws, deck screws, or phosphate flooring screws specifically designed for sub-floor attachment will do the job. Drywall screws will not do the job, and anybody caught using them for this purpose is likely looking to save some money by not purchasing appropriate flooring screws, which cost more money.
Once the subfloor panels are securely fastened with screws to the joists below, the next step to take will be determining your tile backer. This is the material that will sit between the subfloor and the tile itself. Tile is never directly installed directly onto your plywood subfloor; this is because it is difficult to achieve a bond to the wood which expands and contracts, and will result in a failed installation in very short order. Cement board can be used for this purpose, but careful attention to manufacturer's directions must be followed for the installation to be a success. If a contractor uses cement board, they must first trowel (spread) thinset mortar onto the subfloor which the cement board will be laid on top of. This step is very important because the mortar will fill voids and fully support the cement board itself. Once the cement board is screwed down (with appropriate cement board screws), the mortar underneath is spread out and dries, ensuring that there are no gaps between the subfloor and tile backer board. If there were gaps and voids, this would allow movement, and the movement would likely crack your tile and grout.
Contractors utilizing the cement board method like to skip this step because they save time and money, and in the process, contribute to a deeply flawed installation process that almost certainly means your tile floor will fail at some point down the road. Be very skeptical of contractors who try to cut corners claiming to have "always done it this way". Furthermore, any seams between the cement boards must be taped with an alkali resistant mesh tape and filled with thinset mortar. Failure to do so will compromise the strength of the installation at the seams of the boards, opening up the possibility for cracks in the tile and grout down the road - long after the installer is out of sight and not answering your phone calls.
In short: If cement board is going to be used as the tile backer for your new flooring installation, the correct steps must be taken in order to ensure a long lasting installation. This means that the existing subfloor needs to be secured, and the cement board MUST be embedded into a fresh bed of mortar PRIOR to being secured. All joints must be taped with appropriate mesh tape, and coated with thinset to ensure a strong joint. If the proper steps are taken, you will have a successful tile installation!