I think he is actually a great defensive matchup for Dirk. So if Jax can stay out of foul trouble, that increases our odds - as I don't think we have any other particularly good 'cover' for Dirk.
Jackson takes away Dirks ability to drive from the elbow. He will be in his grill at the 3 - where bigger defenders have to sag off for the drive. He is great at stripping him to start the break. he is very physical to knock Dirk off kilter - making him start to force things. And Dirk doesn't have the low-post game to exploit the height advantage. The turnaround fade-away from the elbow is the primary problem due to the height advantage. Last factor is that Jax has the reputation as being physical so he gets some lattitude - particuarly as refs accidentally give sympathy to 'smaller guys' on bigger guys. That just always happens for some reason.
So if Jax is on the floor v. Dirk. We can hang. Any other Warrior defender would get torched by some aspect of Dirk's game.