Hassenhuttl did pressing work at Leipzig but it's far from a given that he'd implement a similar style at Southampton. His Ingolstadt side were boring as fuck, and indeed there were doubts about what Rangnick was even doing hiring him when he's obsessed with sky high octane football. I think it'd take a while before he tries bringing in anything like the Leipzig style of play. Solid, hard to beat will be the order of the day for ages.
Indeed, and that is likely what he'll have to do for the rest of this season to keep them up. Make them horrible to play against and hard to beat.
IF he manages that, then Southampton could be in a very good way.
I know he isn't everyone's cup of tea, but he's a really good coach. Sure, too pragmatic at times, bit of a prickly character too, but he can change teams to play different ways, and when he gets a team pressing and working hard they can be formidable. He did have a lot of good young attacking talent at RBL to do that though, remains to be seen what he can do with Southampton long term. But if they stay up and recruit well, then who knows!
I'd put him above pretty much all but the obvious coaches in the prem. (i.e, Kloppo, Sarri, Guardiola, Emery, Pochetinno, Benitez, maybe Howe). But he needs to do the hard slog to keep 'em up first!