I probably wouldn't count clipping an extension (that doesn't need sewing like wefts) on to a wig as 'styling'. "Moving some hair" is a bit vague since that could either mean fixing hair into place in a mirror yourself, but (as far as styling goes) it's much more than that. There's a shaping to the wig that needs to be done and, for some wigs, you have to take into account if the wig is on a thinner side than most or if it needs wefts or additional work to keep the netting from being seen.
Usually when I do wigs for people (either for friends or on commission), I cut and/or trim, put layers, shape/spray the hair into place (so it won't move), add wefts, and or widows peak as needed/depending on the character. You can offer a commissioner a base wig to work from and they do the character's hair style shaping, but if it's just adding on a pony tail extension that simply clips and is something you can do yourself, I would opt to do that yourself.