In a nutshell, he'd spent the past couple years preparing for these head coaching interview.
For the Green Bay Packers, he was the coach who gave the power point presentation each week, so he'd gotten good at describing his goals.
He'd also spent years putting together a packet of information to explain his philosophy. Via the Journal-Sentinel, from the Miami Herald:
Jeff Ireland said that 15 minutes into Joe Philbin's first interview, he knew the Dolphins were onto something. Stephen Ross said after his interview he talked to Carl Peterson, his long-time friend and adviser, and Peterson told him it was the best presentation by a coach he'd ever seen...
The packet, which Ross indicated is about an inch or two thick, is meant to show teams what Philbin is about. It speaks of Philbin's history, his philosophy …
"Yeah, expectations, values, things in my core belief, base philosophy," he said. "It’s not how we’re going to attack Cover 2 but how we’re going to run an offense. What kind of system we envision running. Are we going to be a multiple formation team. Are we going to be a no-huddle team, things along those lines. More broad based."