Because its hard to discern from his play here what are his PP trademarks. I really and honestly don't know. What facets and plays does he typically bring to a PP. Where is he ideally situated, what have you noted?
Quite honestly I've been disappointed and baffled by the way he's been handled on the PP. I know we see Jesse's career in different lights, and that's fine, but I rather concentrate on what he's done before the NHL as you asked about that. That doesn't mean I believe he can transfer that all automatically to the NHL.
Earlier in his career Puljujarvi has been truly excellent on the PP. To the extent you see rarely. He's been so good that it's hard to imagine something is wrong in the coach if he can't bring that to the level that could at least help the team in two years time.
It's true Puljujarvi hasn't got one clear strength which would make him stand out, which would've helped with his career. However, the combination of how many things he does well or even very well has been very unique. Where he's really shined has been the PP. His shot, when he gets it right, was one of the few I've seen where the goalkeeper hasn't got a chance. He's had a few nasty looking misses, which may have affected TM if it's happened in practises, but he's also been able to hit the puck at a level that not too many players do.
He has also been good at sneaking a bit closer, often to Kurri's place, before firing his shot. Besides this he's been elite at QB'ing, though he's done that a bit less. He's also good at driving the puck across the ice and thus saving valuable PP time. Where he hasn't been used is by the goal, so it feels quite crazy that's how TM has used him.
I still wonder what could've happened if he'd got one or two of the post hits in at the start of his first NHL season. I was sure he'd got another chance later on, but it's been two years since that already. I hope I managed to reply to your question at least passably.