Draw the genus and you get a broad brush: Japan to Australia, the western Pacific, and across into the Indian Ocean as far as Sri Lanka and, thinly, the Bay of Bengal. Draw the species and the brush gets smaller, which is the only way the map stays useful.
H. lunulata takes the tropical middle: Indonesia, the Philippines, New Guinea, the Solomon Islands, Vanuatu, northern Australia, and west toward Sri Lanka. H. maculosa takes the cool south of Australia and Tasmania, including water deep enough that a tide pool is no longer the whole story. H. fasciata takes the east Australian coast from southern Queensland to southern New South Wales. H. nierstraszi is a pin stuck in the Bay of Bengal, not a shaded province.
Those outlines are the published ones, and published outlines move. Animals get carried, photographs get misidentified, and a genus with undescribed members will keep embarrassing a tidy map. What does not move is the kind of place. Wherever a confirmed species is known, it is coastal, shallow by ocean standards, and structurally busy. You will not meet one in a kelp forest off California or on a North Atlantic pier. The rings are an Indo-Pacific story.
That geography is also why the anecdotes cluster. Australian beaches, Indonesian reefs, Japanese shallows, a Singapore incident, a handful of aquarium records. The animal is widespread inside its band and absent outside it. A journal that talks as if the ring octopus were a universal tide-pool resident is borrowing drama from the wrong ocean.