"Dump and chase" is an exaggeration for one thing, if you look at numbers, maybe the difference between the best and worst at O-zone entry is 10% of attempts, and that reflects that bad teams lack players who can execute clean zone entries. Tippett is the best, TK has improved, that's about it right now. And only two D-men can skate zone to zone, Sanheim and Drysdale.
What differentiates most teams is the ability and willingness to make dump and chase work, it requires effective forecheckers with speed and 'tude, Hathaway is one of the best in the NHL. To run an aggressive forecheck, you need speed and size at forward along with the willingness to hit. Anticipating the breakout pass also helps. And once you get the puck and start the cycle, you need to win board battles to maintain puck possession in the O-zone.
Carolina does it by coming in waves, they're relentless, no surprise given Brind'Amour is the HC.
I expect a similar approach by Tocchet, who understand both pressure and skill, you got to get the puck to shoot the puck.