As Jackie wrote, there are many Southern accents. The North Carolina heavy drawl completely changes into the ri-vuh accent of Richmond here in Virginia which has little resemblance to Dinwiddie Southern just south of Richmond that sounds completely different from, say, the accents I've heard come up from Mississippi and that sounds nothing like Alabama ... and so on.

Now this 'ish' sound: I haven't heard this particular one, but I haven't heard every Southern accent. It could be a distinctive sound from one region in the South. I have heard the 'eyezz' cream of which Jackie has written--but I can't remember where. We do enunciate our s's as s's or z's, but I'll start to listen very carefully for that 'sh' to see whether I hear it.