Yes, when the coach is a hold over from the previous GM regime, the pressure is on the coach to conform to the style of play the new GM wants, or he will find himself out of a job by seasons end.
The good news is that Walton coached in a very uptempo system in GSW and had great success.
The reason he may have reverted back to a "slow down" offense last year may have been his desire to "teach" his half-court system to his new team, similar to what Joeger did his first two years. I think the process may have been sped up by having a new GM this year, but I fully expect this years Kings team to be a run and gun, very uptempo team in Walton's 2nd season.