I'm not trying to make this a coaching debate, but I think one thing that i've noticed when comparing his play (from video) throughout his career, he just doesn't seem to jive with the dump and chase style that DJ has the team playing.
When you look at plays that develop off the rush and where they have good and clear possession entering the zone, he looks way more comfortable and creates more and most of his 5v5 goals have come that way.
When you look at all other zone entries that go the dump and chase way (as wanted by DJ) when his line is on the ice the play usually dies because it ruins his flow, there isn't anyone on his line that can drive down to get the puck to get puck control in the zone and all you get is a broken play. For Timmy's line it's generally the same but they have more success driving down and retrieving the puck to get some sort of control in the zone. (but the dump and chase is still not great for them either and that's one of the reasons we're not doing as well this season on 5v5 scoring)
not trying to make this a coaching discussion, but just saying that it really is one of the reasons why he is personally struggling a bit more this year.
I'm sure he likes the guys and the team structure, the city and all of that, but he probably feels the play style being set out doesn't suit him the most or at the very least, he didn't have time to adjust his play style with the trade coming unexpectedly to him as he said.