Grammatically, dont is a relative pronoun the preposition de built in: it's usually equivalent to one of “de qui”, “de quoi”, “duquel”, etc. (but in a given case, maybe only one of dont or “de …” is idiomatic). The only plausible antecedent for the pronoun is “volume”. So yes, this does mean “… volume whose water is …” (except that “whose” is not necessarily idiomatic in English: it's the water “of” the volume, but in English it's more idiomatic to talk about the water “in” the volume).
I guess your difficulty is actually with “volume”? Here, it means a span of space, not the number of cubic meters that this space occupies. The English word “volume” also has this meaning, but maybe less commonly (it's more common with “area”, e.g. when it means “neighborhood”). So the relative clause is about the water of this space, i.e. the sentence is about what happens to water when it's inside this space.
An idiomatic translation in English would be something like “In fact, it is rather a space in which the water is constantly stirred by ocean currents”.