There is no difference between 'physical initiative' and 'matrix AR initiative'. If you're using the matrix in AR, then you're active in the physical world and moving at your own meat speeds. And if your meat is faster than normal, then you work the matrix faster in AR.
This is how adepts can be excellent deckers (and were a very good hacker build in SR4), as well as those who choose to not put themselves in the way of the worst of black IC by keeping their neurons out of VR.