Not actually thinking this is a terrible decision, and wouldn't be surprised if it paid off handsomely for Southampton. The only problem is, he doesn't speak English. However if they can get a new manager bounce Ramos style to stay up this season, and he can learn it well enough for them next season, he could do very well. It's clear that like Levy, Cortese wanted someone more in tune with his vision and that is ultimately a good reason to sack someone, for the long term good. This guy did good things with Espanyol's youth set up, he has been praised for his tactics and is highly rated in Spain with Guardiola being a fan. If they can stay up this year I reckon they've got a good chance of establishing themselves in the league next year under him.
I actually think the new manager bounce comes a lot from a change in playing style which takes opponents off guard, the same players are being deployed in slightly different ways and the margins shift a bit in the team's favour, with opponents taking a while to figure out how to combat the new way of playing. Couple that with the more psychological elements with everyone being keen to impress and they could well stay up. Unfortunate for Adkins but his reputation won't have suffered, he's got a nice pay off and will probably get another good job. I'm not sure it will be in the PL but a Championship club with ambition will snap him up no problem if he doesn't get a top flight job.