I think it can have a lot to do with the players.
The Bruins room took shape under Chara and Bergeron, and they formed the culture and held it despite the stupidity of Chiarelli, Benning, and Sweeney. They've run through a lot of coaches in that span.
The Jackets culture of the previous decade is often mistakenly attributed to Torts, but it was formed long before Torts, and it wasn't because of Todd Richards either. It was around 2012-2013 when Foligno and Dubinsky joined the room with vets like Letestu. The expectations rose across the lineup.
For the current Jackets, they lost their consistent veterans and the lineup filled up with RFA kids finding their way, and frequently lost players like Laine and Roslovic who aren't leaders (not necessarily bad player but not leaders). Boone aside, we don't have standard setters playing higher up in the lineup.
Either way, I don't think JD was a part of the culture problem and I don't think Waddell is going to change it one way or the other through his personal bearing. Maybe through player changes. Maybe through the coach.