Unfortunately, there still isn't a lot of understanding ab out the causes of SPD. which is probably why you are getting conflicting information about it. Having only been defined in the (70's I think), not a lot of testing has happened (studies in behavior psychology just take longer. There are limitations to what this science can do - particularly when working with children and with a disorder that is not extremely common).
The children with whom I have worked that had this disorder were of the SMD (Sensory Modulation) type and had a hard time with responding well to different types of sensations in an appropriate way. One of the kids was a toddler and two - the others were all Middle School Students (adolescents).
At two (the age of the toddler I worked with), kids aren't expected to jump or run well anyway, so did not have a lot to do with helping this child with these skills (so I don't know if the rest of this will apply). However, he was working with a coach and she came into the classroom with him often. She really appreciated every "sensory" experience I could offer the child because he had a hard time with over-reacting to just about any new sensation. Finger painting, running his hands through shaving cream, using playdough, playing with leaves, feathers, fabric scraps (with a huge variety of fabric types - cotton, polyester, silk, rayon, linen, hemp, etc). Once he started getting used to participating in these activities he also found many of them relaxing - though his first reaction was often to be violently reluctant.
If for no other reason, I'd recommend working with a sensory integration coach simply because they are experienced and knowledgable about working with these kids and whatever help they can offer is better than none. They also offer parents and other care-workers help and support with ideas about how to help the child and help the adult carer in coping with the particulars in working with a child with SPD.