I can't tell you how big a sandbed they would need because there are a lot of different species sold as sand sifters and they have very different dietary requirements and maximum sizes. Some might be fine for a very long time in a 125, while others would basically be starving from the moment they were added to the tank, regardless of its size.
Some are so general in their diets that analysis of their stomach contents has been used as a proxy for sampling the infaunal diversity, while others are so picky that they only eat a few species of inverts within a specific size range. Those species closer to the former end of the spectrum would be more durable in captivity, but would also be the most destructive to a functional sandbed. At the latter end of the spectrum are species that would be essentially impossible to keep in a home aquarium of any size.
Regardless of where they fall on the spectrum, it usually takes a year or more for them to starve to death, and any claim of success short of the 2 year mark is probably premature. I generally would not recommend these stars to anyone especially a beginner, given that keeping one generally entails a trade-off between a healthy sandbed or a healthy star.
The answer I typically give about stars is that most people should stick to brittle/serpent stars. If you have a large, established tank and are confident in your ability to keep salinity and pH fairly stable, you might consider a Linckia, but only if you can find one that's plump and flawless after at least 2 weeks at the store. The exception to that rule is Linckia multifora, which consistently does well and even reproduces in tanks as small as 65 gallons.