Unless your LFS has one super-duper curing tub then the time spent at the store doesn't really help it become mature. If anything it can actually make it get worse over time if it comes in good and then is deprived of high light and such. I do know of one shop though with an outstanding LR bin where the rock that comes out is better than what's in most people's mature tanks, so it happens, but the rock from a system like that doesn't look like the rock in the picture. If that's what most of the rock looks like, then it's pretty devoid of a lot of the microfauna that these stars feed on. There will be some, just very unlikely to be enough to keep the star going long-term.
You can try putting various foods near the star, but odds are it will ignore them. It's worth trying though; you could get lucky. I recently saw a "sand-sifting" star eat a prawn (and...guess what, they don't sift when happy LOL but they do clean the sand surface at least). The diets of film-feeders are very poorly understood for the most part. For example, there are some Echinasters that were thought to be film feeders until recently when a gut content study showed they're eating plankton somehow in the wild. So...when I say the diets are poorly understood on these critters, it's REALLY poorly understood!