My first guess is the grout has not been sealed. No tile grout is waterproof, so everytime it gets wet, some of the water penetrates the grout and reaches the backerboard. Over time, this will destroy everything you just paid to have installed.
Go to your local bid box store, or a tile store, and look for grout sealer. Red Devil makes a pretty convenient one, but any silicone based sealer will do the trick. Follow the directions closely, because it won't work if the grout is real dirty, etc.
As far as the "white" problem, think about what you see when you look at bricks exposed to the weather. Understanding that I am making an educated guess here, and anyone else is invited to correct me, I believe the white is being leached out of the grout by the water. Sealing the grout should stop this or at least minimize it.
Again, I am only guessing here, so don't let me be the final answer on your topic. Your tile installer might have a guess or two, and you might contact the grout manufacturer as well.
Best of luck to you!
PS If you have grout in your shower or bathtub surround, you absolutely want to seal these areas for the reasons I described above.