Did a managerial change help? Yes, by virtue of having a new manager, and also by extension having a new hitting coach.
However, the managerial change has overshadowed some other major influences:
Dunn's turnaround may be at least somewhat, if not mostly due to personal issues
Peavy's turnaround is mostly due to being healthier.
Sale and Viciedo have gotten a year older and grown into their new roles.
Youkilis was brought in because of two injuries--his own, that made him expendable in Boston, and Morel's, which forced a move that may or may not have otherwise been made.
Rios' turnaround may or may not be related to a new manager and/or hitting coach, but he's also been very up and down throughout his entire career.
Injury to Danks gave Quintana a chance he might otherwise have never had.
I'm not saying Robin isn't doing a great job--he is, but he's benefited a lot from player development within the organization and some dumb luck injuries.