I've had a modicum of success keeping Purple Tilefish, and have resigned myself that Flashing tiles are just too temperamental (for me) to keep long term. Tilefish are jumpers, so make sure that the tank is well covered. They need a hiding place in the sand, usually beneath a rock or in a small crevice or cave, and can be easily startled; so treat your new one gently.
I've had good success feeding PE Mysis, Krill, Plankton and other meaty foods. Mine have always preferred to feed mid-water, never from the surface and infrequently from the bottom.
-Rob