A few people have reported this behavior. It is most notable between Tangs and sand sifting fishes.
One explanation is that the Tang can benefit by the bottom dweller stirring up pods. The bottom dweller can only 'catch' so much and the Tang is hoping for the left overs.
Currently, my Chevron Tang (now adult) will follow behind my Orangespotted Diamond Goby (an oldie -- 4 inches) and do the same thing. The Goby gets a bit 'anxious' about this and sometimes hops ahead of the Tang, not stopping to sift. The Tang goes by but may start the slow mo chase again. I note this only happens with them in the morning, before their first feeding.
The Chevron Tang now imitates the Goby and does some mock sand sifting too.
The reaction of the Goby, Mandarin, or other bottom dweller can be a mixed bag, depending upon how 'secure' they feel about their tank mate. To the Tang, the bottom dweller is a potential source of food.
The behavior of captive marine fishes is almost a study unto itself. We see things not seen in the wild and things in the wild don't translate into the captive setting.
One thing Mother Nature insists upon -- no behavior is repeated over and over again without there being some benefit to it. Energy is not expended without a gain. Humans may not be able to understand the benefit or advantage or meaning of the behavior, but at its core is some benefit.
