Defensive minded, protect 1 goal lead with 2 periods to go, low scoring teams.
*I'm prefacing this based on Tippett's time in AZ, not his EDM days but I don't believe he was well received there either.
I just looked at the goals scored for each of his teams and where they ranked compared to the team before he got there and compared to the rest of the league while he was there. To cherry pick his last few years in the desert for a dysfunctional franchise that offered him a dearth of talent or support is exceedingly disingenuous.
Without getting into all the details I found:
Tippett took over an offense in Dallas that had ranked 15th the year before he got there. During his tenure they ranked anywhere from 5th to 21st.
Tippett took over an offense in Arizona that had ranked 26th the year before he got there. During his tenure they ranked anywhere from 14th to 24th (the last season they ranked a woeful 29th) but I am sure you remember just how insanely disastrous that organization was. If anything, he helped that team punch way above its weight...he and Shane Doan were the only respectable things about that club during that tenure.
In Edmonton, Tippett took over an offense that had ranked 20th in the league before he got there. 20th! With that offensive talent they were 20th. During his tenure they ranked 11th, 7th and 7th.
I think it's safe to say he is not an offensive genius but he doesn't hold them down either. He clearly played to his team's strengths to produce the most successful results he possibly could (structure, something that was lacking under Lars). I also got the impression from reading a few articles he was liked by his players. So a coach who is liked but not running a circus sounds pretty good to me. He might not have a SC (yet) but the guy has had success in this league.
So if we want a guy with experience, check. If we want a guy who has had success, check. If we want a guy players don't detest, check. If we want a guy who expects accountability, check.