I'm going to be the wet blanket here. Every coach in history after taking over a team says he will play more up-tempo.
It's universal bologna.
Maybe Hurley really does mean it. Maybe he sees the UConn personnel is suited to it and it's the jolt necessary to get them to play more active and tougher.
But Hurley hasn't had a team in the top 150 (55th percentile or higher) in offensive tempo ever as a coach. He's had up-tempo defensive teams, for sure, but his offensive execution has been more... methodical and workman-like. Ollie's teams' offensive possession length was quite slow and on average ranked 226th in the country. While Hurley's over his 8 coaching seasons has been... 230th. Slower.
Defense is indeed a different story, as I mentioned he has had defensive teams that produced quite short defensive possession lengths and got after people, but even with that it never led to "get[ting] the ball down the court quickly". Nor were his offenses ever very effective when his teams played quick paced defense anyways: in the 4 years that qualify the highest his team's offense ranked in the country was 130th.