These jets are a fairly compact stream of particles which are being expelled from the poles of a rotating black hole along a line which extends from the axis of rotation.
What they are saying is that a suspiciously large number of these particle streams are aligned [with each other] even across galactic distances. Secondarily to that, the alignment also happens to be parallel to the line of the cosmic thread.
I'm not sure why you keep getting tangled up on "alignment". It seems pretty straight forward to me. Am I misunderstanding you in some way, or missing something?