Hmm...
Whilst there is technically no immediate reason for something beyond dimensions to have control over them, that's only if we're focusing solely on that definition of being beyond dimensionality. If we extend our thinking to other similar abilities - namely, Dimensional Entity Physiology, which Beyond Dimensional Physiology essentially serves as the logical endpoint of - we can consider that higher dimensional entities are widely considered in fiction to be capable of "[influencing] higher-dimensional and lower-dimensional objects and spaces". If we take this idea to its logical endpoint in the same way that BDP is to Dimensional Entity Physiology, we can consider that BDP could very well possess virtually limitless control and influence over all dimensions and all that is bound by them. I don't know if this control would be considered 'absolute' so much as it would be infinite, but you get my point.
I can only agree with BDP having the highest level of Acausality if we're talking about causality on a conceptual/metaphysical level, in which case it would depend on the verse as to how linked causality and time are. In some, causality exists entirely within the confines of time, in which case being beyond all dimensions of time would easily lead to this kind of acausality. In others, causality is able to operate beyond the confines of time (see abilities such as Origin Manipulation, where the cause provided by the power can lead to an effect at a different point in time, or beyond time altogether). If we're thinking about Acausality as it is defined on vsbattles, it suggests in the highest version of acausality that "Being completely independent of time or laws; or similar forces, does not make you completely independent of causality without the relationship between these forces and causality being clarified, with it only being considered as evidence for an irregular relationship with causality otherwise", which I think expresses my thoughts on this quite well.