I think the assumption is that if the Jazz let go of Rubio in the first place it'll be because they think Exum is their future going forward at the spot or they can get a significant upgrade. Lin isn't a significant upgrade he just brings a different skillset to Rubio (he might be a slight downgrade potentially), and because he's got some size and can shoot pretty well both off catch and shoots and pull ups, I think he's ideal at a 6th man for the Jazz as he can play with both Exum or Mitchell, or play with both. You can still find plenty of minutes for him in that role if he can handle it.
I also have some questions over his play with the Hawks, like his efficiency this year is at 63.0TS% which is significantly higher than any other season in his career (closest is 57.2TS% with Houston a while ago, I'm excluding last season since it's a one game sample size) so what is the reason behind that? Is it because he's playing the least amount of minutes per game since his rookie season? Can he do that night in night out with starters minutes in the West? Is he starting to lose some of his athleticism/1st step now that he's into his 30s and had significant injuries in the last few years?
I'm skeptical that he would be a better starter than Exum for the Jazz. Again it's worth mentioning that the assumption would be that if they let Rubio go it's because they think Exum is the future at PG for them, so you have to assume that his recent stretch before the ankle sprain would become somewhat the norm for the Jazz to do a move like this in the first place.
edit: Lin's efficiency also completely plummets on the road to a still very respectable 56.9TS%, but he shoots an absolutely ridiculous 70.7TS% at home. I just have a hard time believing these numbers are legit considering historically he's been around 55TS% for his career and he's entering his 30s.