It is just idiosyncrasy of practice and learned behavior, and it almost certainly has little-or-nothing to do with some genetically-determined asymmetry within one's vestibular system. Humans of the same handedness prefer to spin one way, or the other, and footedness and handedness are often not shared on the same side. It's like preference for holding the phone with one hand, or turning in one direction during a startle reflex, or using a tool such as a hammer with a preferred hand. All these are reversible with training and the less dominant side is eminently trainable, even beyond the comfort level of the dominant side. To my knowledge there are no studies that would indicate otherwise (hence the "lack of sources" mentioned in the comments). I think the reason that we have sidedness, or handedness for instance, is because of small initial preferences being reinforced, conditioning, and habit. These of course can present as differences in relative nerve or muscle or tendon sizes - however, I stress that these are very individual-specific and subject to change throughout life, i.e. idiosyncratic and plastic.
Here is a review from 2019 from Marcori et al. which goes into some of the underlying neurological phenomena, which tries to detail exactly how dynamically handedness can change. It is only a primer and does not delve into the sidedness that you specifically ask about (spinning) nor the vast majority of sidednesses that you may allude to.
Everyone has some deep, personal experience with their vestibular experiences, be it during exercise, sport or movement, so I feel a comparison of a few anecdotes can do this topic justice, for the sake of understanding the variety of experiences humans have.
If I may: I have a natural preference for keeping balance in counterclockwise spinning, unlike you. Though like you, I am right handed, right footed, and with board sports I ride goofy stance, which is less common than regular stance. With practice you can very obviously and overtly build comfort for the 'lesser preference'. Time spent playing team sports has resulted in a high degree of ambidexterity (confidence, or comfort) in both arms and legs, but with skateboarding, a newer hobby (which incidentally require a considerable degree of 'detaching yourself from the ground', as well as lateral motion, both being new and unfamiliar sensations), I find myself far from able to comfortably ride fakie or in switch stances (with weak foot toward direction of motion, for goofy riders). They are very alien feelings, just as kicking or throwing a ball used to be with my less dominant limbs. There are right-handed musicians that play left-handed instruments (e.g. guitars) and vice versa. The same goes for archers, martial arts, the list is surely endless. There are myriad examples that disprove your suggestion, so I hope that you now better understand that there is no universality, and that the extent of your suggestion was limited in the first place.
However, to elaborate on the biology of things... Certainly at the neural (circuitry) level, and perhaps even within the vestibular system, there are - and must be - differences that cause you to have a preference. Preferences are ultimately physiological, and the fact that you turn this way or that to cover your face from incoming objects is not completely random or indeterministic. But there is no universality that you suggest for a certain direction among humans, especially for spinning or correcting for experienced centrifugal force. Even handedness, which to us may seem fixed, is not fixed; in many parts of the world, left-handed writing was frowned upon and children were forced to write with their right hands, and became right-hand dominant. Certainly some folks from the older generations have experienced this first hand and can attest to how plastic handedness can be.