Okina's ability is her power over backdoors : beside creating them, she can also move stuff through them, seasonal energies included. The season related attacks of hers make use of these seasonal energies in some way. Think of ULiL for example : the heroines get to use brand new occult attacks, kinda fueled by occult power : these seasonal attacks kinda go along these lines, save for the occult part.
But it's not exclusive to her : the heroines in HSiFS use and rely on seasonal energy as well (hence the peculiar aesthetics of shot types and bombs), but the heroines only get to use seasonal weaponry and powers thanks to the season door attached to them, and that door is hers : Okina can pump the seasonal energy that was gathered by the heroines on their way, and similarly to the heroines, Okina can also make use of those seasonal energies. So, regarding the abilities she get to display in stage 6, I'd say these season related attacks are pretty much the equivalent of occult attacks, but for seasons.
The thing is, that is only indicative of Okina being able to make use of seasonal energies, the same as everyone else, and that is regardless of any power over seasons (for example, the heroines can use seasonal energies as well despite not having some kind of season manipulating ability). So, does she have an ability to exert direct control over seasons or to manipulate them in some way ? That's incertain, but she definitely can influence it in some way through her power over lifeforce, delegated to Mai, when used in the same way it was used to cause the incident. There can also be some speculations regarding those suspicious, season colored energy tails that oozes from her even in the extra stage (where she doesn't even use seasons), although I doubt them having some kind of super important meaning.
Can she directly manipulate seasons ? That'd be a big, fat question mark, as far as I am concerned (probably not tbh, save for her lifeforce powers). But what is certain is that her fancy, colorful attacks from stage 6 just derives from a clever use of her backdoor powers plus seasonal energy. At any rate, it'd be pretty safe to stay with what has been explicitly mentionned and just stick with her backdooring ability. Maybe some precisions will be brought when the next Strange CoOW come out.