Elf, if you look at that quilt on Pinerest, you will see that the white diamonds actually 'touch' two blocks. They snuggle together. So, you will not be adding more white background, they will be sharing that white and the next piece will be the color of the star next to it. Y seams are not the easiest to start with for sure, but not impossible. It would help if you had someone to show you how face to face. Hard to describe on paper/text!
This site has the layout, but she is hand piecing hers...but you can see how the white diamonds snuggle in...
http://darlingadventures.com/?p=394
I looked for about 15 mins, but could not find a tutorial on this pattern done by machine.